I like helping people. I adapt myself to all kind of environments I get into. I am on good terms with people. I make friends quickly. I am warm-blooded. I don't like people who lie. I have self-confidence. I defend myself in difficult situations.
Yes you are right "adapt" will suit better. But maybe I think it is better to use the word "defend" or something gives the close meaning at least, because "manage to solve" will be too much assertive and "knowing how to handle difficult situations" might be a kind of interpretation, according to the original.
What about "I protect myself..." ?
I think everything's fine as it is right now, but the sentence "I don't like who lies" is incorrect in English. It should be "I don't like people who lie."