How does Indy know not to look in the Ark? Because it says so in The Bible; 1 Samuel 6:19note "But God struck down some of the inhabitants of Beth Shemesh, putting seventy of them to death because they looked into the Ark of the Lord. The people mourned because of the heavy blow the Lord had dealt them." to be exact.
Early on in the film, Indy even displays his Biblical knowledge when he chides the US intelligence officers ("Didn't you guys ever go to Sunday school?"). Clearly, Indy did his homework better than Belloq, because he knew he had to close his eyes to be spared by the Ark's power. Hardly surprising, though, as Belloq's entire archaeological career is built on following Indy and stealing the stuff he finds.
Doubly so when he seems disappointed that there is nothing but sand in the Ark. Moses smashed the first set of stone tablets in rage when he came down from the Mountain. Which meant the Ark had the second set of tablets combined with the broken pieces of the first set and carried around the desert for forty years. It was a divine rock tumbler!
His refusal to also blow up the Ark is an act of faith in God and the Truth to the power of the Ark. While Belloq correctly calls it a historical treasure that Indy couldn't bring himself to destroy, Indiana realizes if the Nazis do open the Ark, it will destroy them, like the aforementioned passage. He just needs to have faith in God acting out like that once more.
Belloq mentions that he thinks the Nazis are after the Ark because any army that carried it into battle was always victorious. Had he actually read the Bible, he'd know that every time the army (God's chosen people included!) carried the Ark into battle without God's specific direction to do so, they were SOUNDLY trounced and usually lost the Ark as well.
One explanation for the Ark killing nearly everyone present? Despite dressing in ritualistic Kohen (priest) attire and reciting a blessing for opening the Ark, Belloq presumably didn't undergo any ritual priestly purification, in addition to which he's not even Jewish, let alone a Kohen Levite (the only tribe permitted to serve as priests). Without any actual Kohanim present, any attempt to open the Ark is doomed to fail.
When reciting the prayer, Belloq also manages to omit the last part of the prayer, which consists of a blessing to the Jewish people. Quite possibly because he's in cahoots with the Nazis.
Not only that, but take a moment to think about who the Nazis had a genocidal agenda against. Then take a moment to think about who they were trying to communicate with, and what He did when His people were subjugated and murdered en masse before.
Raiders chronologically comes after Indiana Jones and the Temple of Doom. Indy may tell Marcus that he doesn't believe in "superstitious nonsense" but he has seen the power of the Sankara Stones himself when he evoked Shiva, the benevolent Hindu god. He isn't willing to believe the stories of the Ark are real, but he knows from experience there's still a possibility. That's why he doesn't blow it up with a bazooka when he has the chance. When they open it and all the lamps blow out, Indy realizes the power of the Ark is real and the only way to survive is from those instructions in the Bible.
The Sankara Stones were also at a fraction of their power (literally, having only three of the five) and more subdued in the way they demonstrated it, with the most overt show being burning the Big Bad. He's aware of the supernatural but he's never seen it outright kill anyone (the stones killed Mola Ram indirectly, as they merely caused him to let go of the remnants of the rope bridge which caused him to fall down the gorge, where he was savaged and eaten by crocodiles).
It's not necessarily the possibility that it's actually full of deific power that stops him from blowing it up. It's that it's a priceless archaeological find. Irreplaceable, historic, and will make him incredibly wealthy and famous to find it.
'Incredibly wealthy' has never been Indy's goal, although his oft-repeated mantra in Temple about "fortune and glory" does indicate a somewhat mercenary attitude.
Indy does still go after the Ark more for its historical significance over its apparent mystical power, possibly because, while the Sankara stones definitely held some kind of power, we also saw Mola Ram do a lot of tricks. Ripping out the heart could be a simple sleight-of-hand gag, the 'black sleep' potion could be any concoction of drugs and chemicals... meaning that while the stones do have some magical power, Indy still wouldn't be totally convinced of the mystic and magical until Raiders, as a lot of what happened in Temple could've been disproven scientifically.
Although it mostly shown God's wrath, there was a blink if you miss moment, when it was all over. Indy and Marion are now free from being tied up, with Indy holding up what was left of the burned rope; after seeing if Marion was OK, they both look at the Ark, with it giving off some kind of gentle glow. God took the time out of His wrath to free the only two people who respected Him enough not to look into the Ark.
Indy's father was a quiet, bookish type, while his mother died when he was young— so where does his reckless daring come from? In Raiders, Marion tries and fails to drink Belloq under the table, then pulls a dinner knife to escape his tent, willing to flee a Nazi camp in the desert without even shoes— a textbook Indy Ploy, suggesting both learned this from her father, Abner.
The Ark burning off the swastika in transit might be a reference to 1 Samuel, when the Philistines captured the Ark and its first and second warning to them was to knock down, then destroy a statue of their god Dagon. Clearly, the Nazis only deserved one warning, but they were warned nonetheless.
Indy's warning to Marion to close her eyes when the Nazis open the Ark doubles as a warning to young or squeamish audience members (and the parents of such) as well, letting them know exactly when to put their hands over their eyes before the most grotesque scene in the movie begins in earnest.
Indy could have been completely wrong when he called the Army brass "bureaucratic fools" who "don't know what they've got." More likely, they know exactly what they have: a religious object that is far too dangerous for anyone to hold. What's the best solution? Crate it up, put a heavy padlock on the crate, throw away the key, stick it in a warehouse, and forget about it. The final shot suggests the feds know how dangerous the Ark is... because they've seen things like this happen many times before. (See below)
Plus the sheer irony that this is at least the second time it's happened, since Indy and Sallah found the Ark buried under heaps of sand and dirt, where nobody would ever find it. History really does repeat itself after all...
After the Nazis steal the Ark from the Bantu Wind, it is possible that the sub did not dive for the entire duration of the voyage to the island (assuming the deleted scene where Indy lashes himself to the periscope with his whip is non-canon). This explains why Indy managed to survive the journey. Historically, U-boats did not stay submerged for extended periods of time and their electric motors would need to be recharged on the surface. Moreover, the U-boats were much faster on the surface— and given time was of the essence for the expedition (especially after what happened at Tanis), it seems Indy just stayed on deck for the ride.
After Indy swaps the bag of dirt for the idol, the room starts collapsing and he runs out, across the poison-dart floor. The darts fly from the wall, like they were supposed to, but keep missing him. Why? Because they were designed to hit someone on the way in, not have already gotten the idol and be on the way out.
Indy gets quite a bit of flak for being a Pinball Protagonist who Wins by Doing Absolutely Nothing in the climax, allowing The Scourge of God to take care of things. But that is actually a common theme in early parts of The Bible: God often instructs His people to (as per 1 Chronicles 20:17) "set yourselves, stand ye still, and see the salvation of the LORD with you". God would then either smite the enemy directly (as in the film) or sow confusion amongst their number, turning them upon each other and leaving the Israelites with mopping up. Many of the fledgling nation's early battles were handled thusly, including the infamous case where God used arbitrary methods to reduce the size of the Israelite army to a couple hundred — just so that they (and their enemies) would have to realize that it was He who was responsible for the victory.
While Indy did win by letting the hubris of the Nazis destroy themselves, there is one action which he is needed for that would have been different: Marion's fate. Had Indy not joined this quest, she would have likely died in her bar when the Nazis came for the pendent. They had her in a tight hold and Toht was about to torture her. It seems unlikely he would leave any witness alive once they got what they needed.
The fact that Belloq doesn’t know that God always hears your thoughts (his comment about the Ark being “a radio for speaking to God”) seems inconsequential at first, but it indicates that he has done pretty much no research on Christianity or the Ark (aside from what it looks like).
Consider how, after all of the trouble Indy went through to get the Ark, it ends up being placed inside of a box in a secret warehouse somewhere. Who's saying that there aren't things that are more dangerous than the Ark inside of that warehouse too? This is confirmed in Indiana Jones and the Kingdom of the Crystal Skull.
While the US Government is probably taking precautions to ensure only appropriate people have access, one wonders how long it will be before someone disrespects the Ark and dies. The bureaucrats certainly don't seem to respect it, and a box in a top-secret warehouse is hardly the proper place for such an important religious artifact.
Alternatively, it is the perfect place for it— out of the way, where it can't be used at all, much less misused. As stated above, whoever took it to Tanis figured that one out and made sure it was well-hidden (in a stone sarcophagus in a concealed temple, no less) before a sandstorm covered the city— and who's to say that that sandstorm wasn't God at work?
Depends on what you mean by "disrespecting" it as well; the Nazis showed disrespect by arrogantly presuming to do what Belloq clearly thought was the equivalent of calling God on His private line ("a radio to God" being his exact words) and start making demands of him when they've got no right to. The Americans, conversely, are clearly not interested in looking inside the box and are just going to file it away somewhere. As long as they don't peek inside, God can probably deal with that.
Just how many highly dangerous and/or magical artifacts have been collected by the US government? The warehouse at the end is enormous and appears to be filled with crates similar to the one the Ark was placed in, and they are all marked with a "Top Secret: Do Not Open" sign.
After Sallah climbs out of the pit where he and Indy found the Ark, the entire rope drops to Indy's feet. Indy looks at the rope with an enraged expression and snarls, "Sallah!" Then Belloq calls down to him, making known that the Nazis have captured them. But for the briefest of moments, Indy seemed to believe Sallah had betrayed him and was planning to leave him there. That he would reach such a conclusion about a man he'd been good friends with for years speaks to Indy's general level of distrust at humanity. It goes along with how quickly he adapts to the two betrayals he experiences in the film's opening segment, as well as to his history with Belloq. It's apparent that Indy is constantly on the alert that someone who befriends him might turn on him at any moment, and in particular, his quickness to assume the worst about Sallah without any second thoughts ("Sallah would never do that to me") suggest it's become second-nature to him to think in those terms. It's a habit that may be beneficial to his survival, but it probably makes it hard for him to bond with other people, and causes him to live life in a perpetual state of paranoia and suspicion toward others.
