How long does it usually take before posts go through
Depends on the owner of the community you are posting in. If they don’t like what you have to say then they may never approve your post.
Are they pending approval from itch staff, game devs or both?
itch.io staff only reviews pending posts in our public community. In some cases we may review pending posts in developer communities that are flagged as spam (think links to viagra ads, presumably not what you’re posting)
Where can I view my posts that are pending approval?
Unfortunately there is no way to list them at this time, you will have to had saved the URL of the page that was displayed to you at the time of posting
Is it possible to edit or delete them while they are in limbo?
No, you can only delete them from the page that was displayed to you after you made the attempted post
Will receive a notification when they go through or are rejected?
No notifications are generated at this time as far as I remember