Mina olen or Olen
When do you use both and when do you use Olen?
To add a bit more explanation... Hän can be dropped sometimes when you answer a question (and so it's very clear who you're talking about). For example:
Onko hän kaunis? (Is s/he beautiful?)
On (kaunis). (Yes. Literally: is (beautiful).)
The adjective doesn't need to be repeated in the answer either, just like the pronoun. In this case I think if you repeat the adjective in the answer, it sounds more admiring of the person's beauty, while just the verb sounds more like a confirmation of a fact. This goes into some finer nuances of the language though.