Do you mean whether you can publish papers in a journal for which you work as reviewer? If other reviewers check your papers, there should be no problem.
There are some does that record (and you can also add yourself) about your work as a reviewer. The one that i immediately think of is Publons. They say how many articles/manuscripts you have reviewed and what is your (average) length.
This depends on the review rules of the journal. In case of blind peer review and when the reviews are not available in open access, you should not make the information on reviewers or the review itself available publicly. You may give the number of papers you have reviewed, but I do not see a place in one's profile where this information can be put.