They mean the same but there could be a slight difference. 'She might be the most selfish person I have ever known,' is more emphatic and shows that you have never known anyone so selfish in your whole life. Generally speaking, when you use 'I have ever ...', you are emphasising the fact. 'She might be the most selfish person I know,' could mean the same but it could also just describe the current situation. It's possible that you used to know a more selfish person, but you don't know them any more.

The first one is stronger. The second one is a little more figurative.

Either one is correct. The difference is nuance. The first is somewhat more emphatic and direct; the second sounds slightly more tentative and is coded for politeness. In the second, the speaker is implying that in the future the speaker might meet other people who are even more selfish and then the "she" might not be the most selfish person the speaker has ever known. Thus it sounds slightly tentative and/or polite.