A few days ago I suggested an edit to a question (Terminal bell without a PC speaker to correct a wrong path). Can I see the review status? The place in the review queue? I may have made the edit as anonymous user.
You can always see the status of all your edit suggestions.
Go to your user page (e.g., click your name at the top of the screen, on the main site).
Look down to the horizontal list of tabs, which looks like this:
Click the ACTIVITY tab. Some more tabs appear under it. Click SUGGESTIONS.
That shows all the edit suggestions you've submitted. You can view the stauts of any one of them by clicking where it says suggested edit in the entry. (If you click the name of the post you edited, it will bring you to that post rather than to the page for your suggestion.)
It doesn't matter that you can't review other people's edits yet. Anyone--even people who are not logged in--can view the status of any suggested edit, if they have the link to it. (For example, here's one of my old suggestions.) And the links are all listed in your list of suggestions.
(There's other ways for low rep or anonymous users to find suggested edits--but for the purpose of checking your own edits, this should be sufficient.)
For suggested edits you make while logged in, you have a profile subpage for that.
You can see any edit once it has been approved or rejected. IIRC if only a preliminary accept or reject has been cast, it is not visible to you.