I have been pretty much going on an editing spree for answers with poor grammar. I want to make sure that it is allowed, since it is telling me I have too many pending edits and now I'm worried... In particular, is this considered spam?
Please don't bulk edit old posts (*). One of the central concepts of the stackexchange site is that edited posts are bumped to the top of the active question page. This normally allows users to easily see if there are posts with new activity, for example if an OP has clarified their question or a post got a new and interesting answer.
Language edits aren't that exciting to see in the active question list. It is understandable that a post here or there might be improved with an edit and that's a nice thing to do. However if done in bulk, they will take over the active question list and re-direct the focus away from posts, which actually need the attention.
If a post is already on the top of the active question page, editing is normally OK. Just keep in mind that as long as you are below 2000 points, 3 people will have to review your edits. So make sure you write understandable edit summaries to make their job easy and take a second to check if your edit is actually useful for the post before causing work for 3 reviewers.
Actually the following does not focus on whether it is allowed, but on whether it needs to be done.
In order to do a proper edit, one needs to get the gist of the posting. If one can get the gist of the posting, why edit it?
In my opinion the posting is the "baby" of the author and if something needs to be done, it is up to the author in first place. Therefore I prefer suggesting edits to the author of a post via chat or comment to doing the edit oneself.
I know that suggesting edits via comments is not 100%ly in line with the company's policy regarding comments. Therefore, nowadays part of my commenting-policy is that I delete comments of mine myself when I realize that they turned obsolete. ;-)
I said "it is up to the author in first place". Of course, if an author of a posting cannot be reached any more, another way of handling the matter is needed.
From time to time with postings of mine I experience someone editing in order to make the text more readable. As English is not my first language I usually am thankful for that. In cases where the gist of the explanation gets distorted/turned into s.th. wrong, I undo the edit and add a note about the subtlety of why the attempt of explaining in the way of the one who edited would yield s.th. wrong. I do so as that info might lead to a better understanding.