Hi, e 1) I’ll do what I think is right. 2 )I’ll do it, which I think is right.
"i" pronoun functioning as subject. "will" is modals OK, although I'd call it an auxiliary verb. "do" main verb. "what is think is right" is direct object. OK. I'd call it a subordinate noun clause. If you want to, you can analyse each word in this clause, too.