I firmly believe that he will be able to defeat Voldemort only by conquering those failing in himself.

Absolutely.

I think Harry wouldn't call Neville fat, because he likes him. It's Neville with the friendly round face for him, no matter if he gained or lost weight, which he very well may have.
Harry uses the weight issue against Dudley, whom he hates. That is an interesting fact. JKR seems to know that "fat" is a better insult than "cruel", after all she lets Harry call Dudley fat all the time, in thoughts and words.

I would say that Harry had a very low self confidence in the beginning of the books but it shot up throughout the series and now he overcompensates in arrogance.

Why do you think that Sirius definitely suffered abuse?