Wow, nice dance number there, but if it took place in a massive auditorium behind the club's stage, and there was no way to televise it back in 1935, who in the club was even able to watch the performance?
It might be Willie's Imagine Spot. This is actually suggested in James Kahn's novelization.
Or just a joke (at the fourth wall's expense) about how they used to shoot extra material (or use recycled material from earlier films) and splice it into movies to make them longer. The obvious break and different quality in video would play into that sort of meta-humor. Remember that these films are send-ups of old pulp serials.
Or a more mundane explanation, there's a movie screen in there and they basically cut to a much bigger pre-filmed dance number that was being projected on the screen.
Temple of Doom is also a prequel to Raiders Of The Lost Ark, which means that Indy being confronted by TWO swordsmen takes place before the famous incident in the marketplace. Indy's gun could've come in handy several points through Temple, and thus it's his first choice in Raiders when a sword-bearing enemy comes across him.
It's also why he appears to carry two guns in Raiders.
Another is ripping out a beating heart. It's all about perspective. When we see it done the first time, it's from the followers' viewpoint, who believe the victim's heart is being ripped out. When we see it tried again, it's from Willie and Indy's perspective, who realise the whole thing is a sham, and don't fall for the trick.
Not to mention the fact that your argument is built on the assumption that any supernatural element in the story means that anything which could be supernatural is. Point in fact, if the heart-ripping really is the result of the power of suggestion(as I am inclined to believe), it makes the actual power of the Stones more spectacular and goes further to explain why the Thugees would want them, i.e. so they no longer have to pretend to have magic powers.
Plus, all the followers were drugged with hallucinagenics so they would believe whatever Mola Ram wanted them to believe.
There's also the factor that he probably didn't rip Willie's heart out, because he wanted to do something more terrible to her. Such as making the brain washed Indy restrain her and lower her to the pit.
Why the stones worked in Indy's favor even though he didn't worship Shiva. The Shaman prayed to Shiva prior to their departure to Pankot to help guide them. So Shiva was on his side, whether he worshiped Shiva or not. As well as the fact that because Indy spoke Hindi, he knew how to invoke Shiva through the stones just by knowing the language. Whilst Mola Ram who was aware of both Shiva and Kali pretty much tarnished the former. Gods get more pissed off at believers tarnishing their truths than those that don't believe in them at all.
The Artistic License regarding Kali worship makes more sense when you consider that Mola Ram is blaspheming Hinduism in universe.
That and the possibility that he doesn't truly believe in the god he claims to worship and that he's simply using his self proclaimed belief to control the other Thugees. Like a real cult.
Why Willie didn't burst into flames when she was closer to the Lava than the last guy? Because at the time the other guy was being sacrificed, Mola Ram had his heart out and was chanting. It was a spell Mola Ram chanting which caused the flames to rise. Whereas when Indy and Short Round were trying to save Willie, Mola Ram escaped and the rest of his chanting followers were busy fighting Indy to invoke Kali.