While there might be some disagreement about what makes a tragic hero, in my opinion, Baba is not a tragic hero. He has some of the requisite elements, for example, being sometimes noble and sometimes virtuous. However, the most common understanding of the tragic hero is that he causes his own downfall because of a fatal flaw. In The Kite Runner, this simply is not the case. Baba certainly has flaws. For example, he clearly had an illicit relationship with Hassan's mother, and he is wrong for sending Ali and Hassan away. However, what happens to Baba and Amir, that they must flee their home, does not really have all that much to do with any fatal flaw in Baba, but is, rather, the consequence of the politics of the country. The fact that he dies after having some good years repairing his relationship with Amir and knowing that Amir and his new wife will have a good life in America also tends to not make him a tragic hero.
I would argue there is a better case for Amir being a tragic hero. He does have a fatal flaw, a kind of cowardice, which haunts him throughout the book until he finally grapples with it. Even then, his cowardice has cost him and many others considerably.
Yes, I would say so. He could be classed as a hero because Amir looks up to him more than anyone else in the novel. The character of Baba also carried out charity work and was generally looked up to in the society he lived in.
Although it could be argued he was not a hero because of the sins he committed, and the way he treated his son Amir.