For example, if you add the prefix dis- to the word like, you get dislike—the opposite of like.

Is dislike a prefix or suffix?

'dis' in dislike ----it's a prefix. So, it is prefix.

Does dislike have a suffix?

I think the best suffix as an answer to your question is -phobe itself. While it may derive from a literal fear of something, in common use it also means simply an aversion or a dislike.