Is there something like a "peer-review paper"? Journals like CVPR (IEEE Conference on Computer Vision and Pattern Recognition) have a peer-reviewing process. Depending on the journal (or the publication published after a conference - is that also called a journal?) one might simply know that all articles were peer-reviewed.

However, those reviews are not publicly available as far as I know.

This is also a problem of arXiv / bad journals. They might have (many) good articles, but one has to check them. A work-around might be to look at citation counts / who cited the article, but citations are not necessarily positive.

Are there any typical / recommended ways to write reviews and make them publicly available?
Depending on whether you want to leave short comments on papers you weren't invited to review or make public full reviews of papers that you were, you might look at http://www.pubpeer.com and http://www.publons.com respectively.