X-Men is a superhero film franchise, not an exercise in deep intellectual discourse on race/gender/et al. They are an important part of the subtext, but the primary focus is on the action/adventure story.
I wasn't expecting a thesis paper...

but it would have been nice for a moment for the actors to suggest some kind of feelings about what had happened. Instead, she returns and smiles at him...? End scene.
Fully formed physically yes, but her power levels increased gradually over time until she lost control and Xavier (much as in the movie) had to put in "psychic circuit breakers".
Those blocks were then eroded thanks to the manipulations of the White Queen and Mastermind on behalf of the Hellfire Club, who wanted Jean to be the new Black Queen.
I don't remember Xavier's breakers, until after Mastermind did his damage... but I believe you. But this argument is the old "If Superman's there, why have a Justice League?" and the answer is "If your writers can't deal with the characters, you need new writers... or a new league." For X3, they *chose* to put Phoenix on screen. So they should try to have her make sense... just a little. Some of the time. If you can't make the character work, you've made the wrong choices. This movie made the wrong choices over and over and over.
Her relationship to him did not result in her death. Logan was the one person who deeply and truly loved her who had the inner strength to do what had to be done to stop her. Pretty boy Scott, for all his declarations of love, could never let her go like that.
Well, be fair. At this point in the movie, Scott is dead.
In the film, Wolverine had to actually kill her himself, since the setup didn't include a handy Kree plasma cannon to destroy herself with.
It just didn't work for me. His quick-healing seemed phony, the idea that she'd just watch him come, that they would give up on every other idea except killing her... it felt contrived and anti-climactic.
The comics did it better - if Phoenix is the ultimate power, then you don't fight with her. Faced with someone she loves, she backs down... or she dies to save them. Those ideas had some emotional power... the movie didn't.
In the movie, she clearly had the power to kill herself, and said she wanted to, and had motivation after killing two people close to her. There were two (then one) power-stealers in the movie. There were lots of better outs than the one they chose.
I thought it rather obvious from the actors' portrayals.
The scene where she jumps Logan was... embarassing. Especially 'cause we don't know where Scott is. Phoenix is entirely opaque all through the movie, so nothing she does seems realistic or moving - it just happens. (with the exception of killing X - which might have used a little more explanation)
Jean is at that point almost psychotically drunk on power, and not in her right mind.
That may be true. But the movie makes no effort to show or even tell us that. It just happens. Why would she start off "psychotically drunk" and then calm all the way down to catatonic? and if she's not acting like a human being, who cares about her anyway?
Hank is a good boy, and his parents were older than many when they had him, so he comes off as being a bit "old fashioned".
I'm just bitching for the sake of bitching with this one.

But really, your explanation does say something to me. You forgive what I see to be a flaw, because you've explained something for yourself, based on what you know about the universe. You did that a couple of times upthread too. That's cool, I guess, but it's not judging the movie on its own merits - you're kind of seeing the tip of an iceberg that you already like. To me, the tip didn't work on its own (and I knew a fair bit of the backstory already). Part of why seeing the Beast on screen is great is because we've always *wanted* to see it. I wonder what non-fans got out of it.