I think there should be a markdown counting of suggestion limit, like how many I applied and how many I've left. Or is it already there and I didn't get it yet?
The easiest way to currently do this is to go to your profile:
and count how many pending edits you have:
before you ask: this is indeed a screenshot made today
Subtract this number from 5 (20 if you're on a beta site), and you have your desired result. Beta sites can be recognized by the word 'Beta' next to their name in the title under the navigation bar (though there are a few exceptions).
It's not a good idea to suggest several edits in a brief space of time.
Let's say you edit 15 posts within 15 minutes, automatically your edits enter the review system where two (or three) users have to approve each one.
Well, if someone sees the same user's name popping up, and if the edits do nothing to improve those posts they might start rejecting the other edits. The opposite is true if the edits are pertinent, useful, suggest significant changes without being invasive, and generally help improve the legibility. When that happens, users will trust your suggestions and approve them more quickly.
Shog9 ♦'s answer to the question Rate limit suggested edits might be of interest
As of a few seconds ago, [Jul 13 '16] this limit is now active network-wide:
at-most 20 pending suggested edits per editor on beta sites
at-most 5 pending suggested edits per editor on graduated sites
These limits are based on my analysis of the speed at which edits are generally approved and the number of edits (and editors) that would have been affected over the past few months.
See also this question Moderators should be able to manually ban users from suggesting edits
I believe six or more rejected edits in a row triggers an automatic ban from suggesting further edits by the system. P.S. I looked for what that specific number was but didn't find one. In any case, you'll want to know before your account is banned whether an edit of yours has been rejected. Read the reason/s why it was rejected and try not to make the same mistake.
To read the reasons visit Profile, click on Activity, then go to the responses tab. Select suggestions where you'll see which edits were approved and which were rejected.
To summarise, take it slow because low-quality, trivial, well-meaning but ungrammatical edits will always be rejected in the review queue.
A much faster way to gain rep is to answer a question.