I don't know this would be appropriate or not, but I would like to draw a comparison with an Indian serial - Chandragupta Maurya - which is supposedly a historical show. In that show, the 10 year old Chandragupta singlehandedly takes on a dozen armed goons - each of whom are twice his height and thrice his age - and beats them to pulp, then jumps off from a 800 ft cliff, masters all types of warfare in mere four days and even coolly walks past a fully grown mountain lion, unscathed. If this is heroism, then certainly Harry is in no way a hero.
Harry is like any other ordinary school going kid - he has his own share of fears, failures and vulnerabilities, which is conspicuously highlighted through out the series. Rowling never intended Harry to be a superhuman hero. Infact in Book 5 and 6 Harry himself wonders how can he possibly hope of defeating the most feared Dark wizard - he neither has any extraordinary skill nor knowledge. Dumbledore replies that he's extraordinary, simply because Voldemort himself made him extraordinary. The prophecy said '..He shall have power the dark lord knows not... The Dark lord shall mark him as his equal..' . This is the catch phrase. Voldemort himself marked Harry as a threat - his equal - and thus made him special. Harry, or for that matter, no wizard could have ever overpowered Voldemort through magical skills, but Voldemort was defeated by a greater power of which he had neither knowledge nor understanding - the power of love and sacrifice.
This plays a crucial role through out the entire series. Our downfall is often hidden in those things which we disdain the most - love, loyalty, friendship, innocence - we, more than often, ignore that they all have a power beyond all physical force or riches one can hope to accumulate. I don't think even the so called matured and realistic novels can give this piece of underlying practical wisdom more tacitly. Perhaps that is why Harry Potter Series, in spite of being a kiddish fantasy, is universally loved and treasured by readers of all ages.
As for Dumbledore appearing partial to Harry, you need to understand that Harry was Dumbledore's trump card in his Grand strategy to bring about Voldy's defeat. He couldn't have afforded Harry's expulsion under any circumstance. Dumbledore had never stopped Harry from his 'nosey' adventures, because, as he would later imply to Snape, he wanted Harry to try his strength and be prepared for the days ahead. Dumbledore had carefully planned his every move around him right from the day he had placed the infant Harry in the care of the Dursleys and even after his own death, he ensured Harry's triumph.