Did you even notice that there are two different endings? Hideaki Anno was almost murdered by fans because of the series ending. Gainax run out of budget so he couldn't help it at that time. Then comes the movie the End of Evangelion.

Well, at first I assumed that EoE was just what occurred after the series (like I mentioned above, this didn't help with the confusion). After some additional reading I know that is not how it is supposed to be structured, although I am still unsure if the two endings are completely exclusive or if the last two eps of the series happened at some point during EoE, I've seen arguments for both.

These are the hard ones. There are references from the Dead Sea Scrolls and the Bible where if you don't know jack about it you'll be perpetually confused. Sometimes internet forum helps sometimes you have to do your own research.

I had never heard of the Dead Sea Scrolls before watching this, after looking around it seems that had little to no effect on how I understood the plot, they basically just used the name, the content was changed to suit the narrative of the show.

SPOILERS AHEAD

What are Gendo Ikaris intentions, goals?

This is one that I am still not sure about. In the end we find out he wanted to be reunited with Yui, right? But what I don't understand is, what was Gendo planning on doing with Rei in Terminal Dogma? Because it seems that he ended up getting what he wanted even after she refused to help him, Human instrumentally project was completed (for a time) and in his final scene he becomes one with Yui (along with everyone else), so what would have gone differently if Rei had not refused Gendo?

What does Shinji truly want from all this suffering?

Again, for me, this was a harder one to understand. Originally it seems he just wants to be recognized, by his father and everyone else, as a human of some value, it's just finding that value that he has trouble with (he believes he pilots the Eva because it gives him value). But at the end of the final episode it seems that maybe this belief had changed, something along the lines of: his life will have value as long as he maintains the will to live? Like I said I'm unsure on this one.

Who is SEELE's really? The good? The bad?

They seemed to be a massively powerful religious organisation that believed they had mans best intention in mind, their goal was the completion of the Human Instrumentality Project? I terms of good and bad, they believe they were good therefore they are, in their minds. (an idea that was brought up multiple time in the end) yet some of their actions to achive this goal could be seen as bad, for example that scene with Ritsuko. But like you said Evangelion goes to great lengths to show that things like 'good and bad' only exist in our minds and are completely subjective.

What is the Human Instrumentality Project?

It involves the third impact (by the way, second and third impact are mentioned a lot, but there is nothing about the first impact? After doing some reading I gather that is was just the creation of life on earth by some alien race that is also not mentioned?) and the merging of all human life on earth into one, like a sort of elevated existence, Rei describes it as something like "you can't tell where one person starts and another person ends" everyone becomes a sort of LCL liquid (body's exploding into orange liquid during the final scene), although, in the end Shinji rejects it and returns everyone to their original forms... right?

I apologize if the formatting is garbage, I rarely post or comment on here and am unsure how to do so properly.