Why can't I review posts anymore?
Because your review privileges have been temporarily revoked, due to a series of bad reviews.
56 of your 57 First Posts reviews have been "No Action Needed", which is a warning sign in itself since some kind of action is usually appropriate. (You can review your reviews here - note that this link works only for you and mods.) And upon looking more closely, some of your reviews were "No Action Needed" on non-answers, where the appropriate course of action would be flagging.
Some of your Close Votes reviews have also been inappropriate: you voted to leave open a couple of story-ID questions contrary to our established policy. I assume this is simply because you weren't aware of the policy, and no harm was done in these cases, but now you know.
on all the questions or answers it only provides
No Action Needed or
Skip. I didn't want to skip the post as I was there to make a review, so I just selected
No Action Needed.
This remark displays a very worryingly poor understanding of the way the review system works. If the only actual review you could make was "No Action Needed", then what would be the point of having the review queue at all? You should have realised that you were misunderstanding the system if you thought there was only one possibility for actually reviewing the post. What you should be doing when reviewing First Posts or Late Answers is taking some action on the post (e.g. voting, flagging, editing, commenting) and only clicking "No Action Needed" if, well, no action is needed. Once you've taken some action, even if it be as simple as upvoting a comment, the "No Action Needed" button will disappear and an "I'm Done" button will appear instead.
but it has already been flagged to get to this point, so why flag it again?
No. In the First Posts review queue, every post by a completely new user shows up for review. The point is that new users are never supposed to be posting into a vacuum, and always get some kind of feedback on their post, which makes them more likely to stick around if the post is good. Same for Late Answers - every new answer to an old question shows up there.
You may be getting mixed up with the Low Quality Posts review queue, in which answers do indeed have to be flagged in order to appear. But in that queue there's no "No Action Needed" option; you can either click "Looks OK" or "Recommend Deletion".
Another important point about First Posts and Late Answers is that you're the only person to review them - a single review is enough to remove them from the queue. That's why it's particularly important that you review these carefully - an inappropriate "No Action Needed" could result in non-answers or spam remaining on the site unnoticed.