I just got an email inviting to review a paper. I have two questions:

1. I realized one of the authors, and probably the most experienced of the authors, is a professor I met months ago in a conference. After that, we have talked several times about working together . Is this coincidence or is there a way to choose or suggest who review your papers?

2. Do you normally put this reviews as part of your academic experience in your CV? Do you specify the journal?

When you submit papers you can choose the reviews and sometimes the journal will use these reviewers and sometimes they don't. You have no way of knowing. It sounds likely the professor named you as a reviewer.

I don't think it's usual to mention articles that you have reviewed on a CV. At least not biology anyway.

Fine to write on CV that you are a peer-reviewer for xxx journal.

Yes, you should put that you have reviewed papers on your CV.