Everything Dragonfree said++++ (as usual)
Whether a character is a Gary Stu or not is less about the character than how you, as the author, relate to the character and, in turn, how the rest of the world relates to them. It's not something you can fix by stapling on a couple of flaws here and there. I mean, the list you have there is more or less okay, albeit vague ("mental struggles"?), but if you're writing in such a way that the character is a Stu anyway, it's probably just going to morph them into some hideous kind of wangst Stu rather than whatever they were before. It doesn't matter whether your character is a nice guy, or good looking, or rich, or powerful, or anything--people have written stories about gods and managed to not make them Stus, so it's not as though relative virtue, power level, etc. actually has a ton to do with it.
The particular scenarios you've presented in your post aren't particularly encouraging. Having the character screw up and learn something from the experience is definitely good, of course. But the way you've described the event it's not really clear what it's going to mean for the development of your story. If your character learns and grows from the experience (and that's important to the rest of the story), then all the better; but if you just have an instance of the character being reckless, then thinking, "Hey, maybe I shouldn't be so reckless anymore!", well, it doesn't really mean anything. It also looks like you're going for a flaw-that-doesn't-matter with the self-doubt thing; having a character question one decision, briefly, then find out that it was okay, he was right all along, isn't really a flaw--if anything, it could just be the narrative validating that the main character is right (as usual).
Overall it looks as though you're looking for things you can kind of shoehorn into the story to have your character going from being a Stu to a not-Stu, but that's not really how it works. Your character having experience X or Y, or particular trait A or B, isn't really relevant--it's how the story as a whole takes shape that matters. Of course, that means writing a character that's not a Stu isn't that easy, since you have to consider the story as a whole, rather than being able to boil things down to easy rules like "don't make your character win every battle." There are rules of thumb (and that's one of them), but they usually address symptoms rather than the underlying problem, which is usually the author's attitude towards that character. But that's probably why it's so common! If you could stop your character from being a Stu by having them doubt themselves now and again, I'm sure they wouldn't be nearly so common.