Is supplicating and giving charity on behalf of one's parents sufficient to fulfill their rights, given the difficulty of direct interaction with them due to their severe injustice? And is the son sinful if he avoids them gracefully (hajran jameelan) to protect himself from anger and harm?

It is not permissible to sever ties with one's parents, even if they commit wrongdoing, and their right to dutifulness remains. You have done well by supplicating for them and giving charity on their behalf. However, not visiting them and not greeting them is an act of undutifulness. Therefore, be patient in visiting them and greeting them.