As far as I can tell, Karna makes much more sense as an Archer than a Lancer. He only seems to be the latter for the sake of being the most suffering Lancer ever.
Many heroes can be summoned as multiple classes. Hercules from Fate/stay night could have been summoned as any class other than Caster, for instance. Karna's description indicates he can be summoned as Lancer, Rider or Archer, and it's possible whoever summoned him wanted him to be able to use his God-slaying lance, which he may not be able to use in other classes or it's possible that the Archer class was already filled up at the time of his summoning.
Much like Hercules it's pretty much a plot device, not a lot of people know this but Karna's bow granted him victory every time he fired it, that coupled with his armor, meant that he would be invincible, with no way for the other Servants to beat him, him being summoned as Lancer is the only way to "make things fair", otherwise he might have been even more broken than Gilgamesh
That's not it. In the Nasuverse, it's just an established fact that Karna's main Class is Lancer because of Vasavi Shakti, that's basically just what the writers decided to go with so they could include other characters as Archers. The Visaya bow granting guaranteed victory wouldn't necessarily happen if he were summoned as an Archer either. Most likely, the effect would just be different in the Nasuverse. Take Excalibur: that's also supposed to make you invincible, and yet do you see how rarely Saber doesn't get destroyed in her fights?
Does Joan of Arc's noble phantasm really kill her, or does it just weaken her considerably if she uses it right ? Cause it seems a bit silly that she can use it only once.
Yes, it kills her. It's the embodiment of her execution. She uses it, she dies.
Atalanta is described as Neutral Evil, yet her motives in the war seems to be Good, trying to create a world where children will be loved. So... which part makes her Evil here? This is getting complicated like how a sociopathic dick like Gilgamesh is referred as Chaotic Good.
Atalanta is most famous for challenging her suitors to a race and then killing them if they lost (which is kind of a dick move, considering she is the fastest human in Greek Myth and knows it). While not actively being "evil" she is ultimately a selfish person as being raised by bears doesn't necessarily make you a good person. whereas Gil is famous for justly ruling the greatest empire on Earth for 125 years by generally being more awesome than anyone else, and while he might seem murderous by today's standards, he was saving his kingdom(which was the entirely of humanity back then) from a piss-off goddess and a Divine Bull, which caused famines and droughts for seven years.
It's a moot point since David is no longer a servant, but since his sling allows him ownership over the target's weapons, what does that mean if he hits Gilgamesh? Does he gain ownership over every weapon in the Gate of Babylon? Does that mean that just Gilgamesh loses ownership of them, or does it also make their original wielders lose ownership of them as well? Or how about Fate/Stay Night Archer? Does it work against Lancelot's improvised weapons? It's clear that the writers didn't think his powers through. This is supposed to be his weakest Noble Phantasm.
Sounds like it. Unfortunately we can't see it in execution (I would guess that he can only steal items that are physically present—he could grab a spear that got thrown at him, but not open the Gate), but based on the Type-Moon wiki's translation, you're right.
The way it's worded on the Type-MOON wiki implies it only works on opponents with weapons at the moment of the sling's use. Arturia with Excalibur? Yoink. Gilgamesh with Gate of Babylon? No. The gate itself isn't the Noble Phantasm, the key used to open it is. As soon as he uses the key to open the gate, it disappears. Lancelot with Knight of Honor weapons? Sure, why not? Doesn't mean he can't make more though.
Achilles invulnerability. What does being divine have anything to do with bypassing it? Shouldn't it be just his heel?
It is explained that in the Fate universe, Achilles' invulnerability was granted to him by the gods, therefore only gods or those similarly empowered by them could actually harm him.
This is kind of a moot point due to it already being done, but wouldn't it make more sense for Fiore to summon Heracles? Granted the arrow killed Chiron but it was shot by Heracles, strategically that would have made much more sense, and wouldn't that have been awesome? The two greatest Heroes of Greek Mythology in their respective best classes in a fight to the death to prove which one is the better hero?
Maybe, but, it´s as you said, it killed Chiron and was shot by Heracles. That connects the arrow to both heroes and either could be summoned, but Chiron must have been more of Fiore's speed, kinda like what happened with Kairi, who used a fragment of the Round Table and summoned Mordred.
Using catalysts that are related to multiple heroes is basically a roll of the dice. However, it also appears to be that if there are multiple choices, the Grail will simply choose the hero that is personally best suited to the summoner. Chiron and Fiore ended up being a good match for each other, and it would be very hard to argue that Kairi would have gotten along with any Knight of the Round Table other than Mordred.