And furthermore, pursuant to your observation regarding Harry’s luck, my instinct at this point is to simply say that that is what will happen in a children’s book, that the main characters will have a Tintin-like stroke of luck at moments of great peril, but, this being Harry Potter, such conjecture is unworthy.
So instead –
Firstly, you don’t give Harry enough credit. In almost every book he displays exceptional powers of deduction, as well as other traits such as being an accomplished wizard and possessing great bravery. In the first to discover the secrets of the Stone, battle through to the end, in the second to find the Chamber, and battle Voldermort alone, in the third to find out about Sirius, as well as rescuing him, in the fourth… well not much in the fourth, but he certainly displays initiative. In the fifth he is deliberately misled, but does sterling work with the DA, proving that he is a better wizard then one might have realised, when you see how far advanced he is ahead of his peers. In the sixth, his rescue of Dumbledore at the end was impressive, and in the seventh, he outsmarts one of the cleverest wizards ever, and that was almost completely without help. So to sum up, he does display many talents through the book, even if he does get a lot of help. And that was even if you ignore Hermione’s help.
Secondly, many of these strokes of luck are deliberate design, by other, greater wizards. There is strong evidence, and often explicit proof, that Dumbledore was aware of many of Harry’s challenges, but chose to let him face them apparently alone, but help him in indirect ways. For example, Fawkes in the second book. Add to that Voldermort and Crouch manipulating him, and much of luck is proven to be anything but.
And there is more to be said on a more general point of JK deliberately not writing Harry as a genius, but that can come later. And I join yekke2 in urging you to read Harry Potter and the Method of Rationality, which does exactly that.