Can I fix my dad's papers even though he has a felony charge?

Your question requires an attorney consultation. It is not a simple question that can be answered on this type of forum. There are many factors that would need to be considered and evaluated. The short answer is that it depends on what the felony conviction was for. I strongly suggest that you contact an experienced immigration attorney for a face-to-face consultation and give him/her all of the facts surrounding your father's case.