I am seeing this red dot beside Low Quality Posts, but when I click it, there is nothing inside to review. So why is it showing? Am I yet not eligible to review low quality posts fully?
There are currently two items in the Low Quality Posts review queue (you could check that by opening another browser, or a private/incognito window, so that the site doesn't know you're logged in; another way is to use the Wayback Machine).
You can't review Low Quality Posts review items for posts you've already flagged, and if you skipped the item you won't see it again either. However, the red dot is calculated and cached on system level (it would be too expensive to do this on a user-by-user basis), that's why you do see the red dot.