Are reviewers chosen from among the editorial board of a journal?

Generally, when a paper is submitted to a journal it is first assigned an editor. The editor then identifies a qualified outside reviewer for that particular manuscript, and invites him/her to review the paper.

So the answer is: No, you should not expect that the possible reviewers of a paper are selected from among the members of the editorial board.

The purpose of peer review is to obtain constructive evaluation of the submitted manuscript from peers who are experts in the field free from conflicts of interest relative to the manuscript and author(s). Hence it is essentially irrelevant if the reviewer is one of the editors. That said, it is very unlikely that an editor ends up reviewing a paper for two reasons. If the editor is an expert, it is far more likely he will be the editor for the manuscript. An editor, with, probably, much work to to do with other manuscripts, is also less inclined to take n review work unless the manuscript is of particular interest. So chances are quite small.

In the journal I edit, I know editors have accepted reviewing the topic. In these cases, the topic has been such that it has been given to another editor who have identified the other editor as a potentially valuable reviewer. Commenting on your comment: I would expect editors to be more punctual with reviews than "normal" reviewers but there is no rule without the occasional exception.

A final comment. I do of course not know how the journal you have submitted to works. But, a normal case is for a Chief Editor to pass on the task of assigning and evaluating reviews to an Editorial Board or Associate Editors (as is the name for them in "my" journal). I think the case of a Chief Editor doing all that work is very unlikely because of all the work involved so it seems far more likely that it is one of the editorial board who is handling the review process. The Chief Editor may be involved in screening submissions and putting a final stamp of approval to the final manuscript as well as handling all the work visavi the publisher.