What were the Pandavas fighting for?

There are four possibilities:

1. To get the kingdom of Hastinapura and become kings.
2. To take revenge for Draupadi's insult.
3. To uproot adharma from society and establish dharma.
4. They had no clue and were doing only what Krishna told them to.

Lets examine each of these one by one.

Is there a peaceful religion?

Violence is as old as the age of the universe and religion is as old as the first human civilisation. Since time immemorial, religion has led to some of the most peaceful people (Buddha, Christ, etc) and also to some of the most violent ones (Hitler, Osama, etc). In modern times, it is usual practice to designate every instance of religious violence to a misinterpretation of scriptures of that particular religion. But is this always true? Is there any religion that is totally against all forms of violence?