Could this site somehow let contributors know if a homework and exercise question has been reviewed and found acceptable for answering? Right now we only know when a question is found to be unacceptable and put on hold (sometimes after spending considerable time answering it). I would like to wait before answering these questions until I know they have been found acceptable for answering.
This isn't workable. The process to "certify" that a given post is on-topic would require a consensus of 3k+ users, almost certainly via a review queue, and there is no realistic way to make this happen faster than the existing Close Votes review queue.
The real problem is that the Close Votes review queue isn't currently as fast as we would like it to, particularly for the obvious broken-window questions like blatant homework dumps. Ideally, we'd like those questions to be closed before anyone has time to post (or even start writing) answers for them, but the current reality is that it's not happening that fast. The solution to that problem requires more reviewer time, and diverting reviewer time to a separate queue would be counter-productive.
If you want to know whether a post violates the homework policy enough to be closed because of it, there's a straightforward alternative: read and understand the policy and come to your own determination of whether it's in direct contradiction to those principles. Unfortunately, of course, the stated policy is only an imperfect capture of the actual real-world application; I wish I could tell you that that's about to be fixed but the reality is that the homework-policy debate has taken so long and drained so much energy (see the links here for an incomplete sampler) that the chances of movement on that front in the near future are slim. Still, as you see more of the site, you'll be able to get a sense for what does and does not constitute an about-to-be-closed homework question.
And, as pointed out in a comment below Chair's answer, if in doubt, head over to the site chatroom and ask. We can't promise to provide a definite answer, but it's quite likely that we'll be able to give a reasonably accurate prediction, together with an explanation of why it falls in either class of question.
I don't think anything similar can be feasibly implemented. It has been suggested on Meta Stack Exchange that we implement a system by which posts are made publicly view-able only once they have been reviewed. With such a system, you won't see any homework questions in the first place. But those proposals weren't well-received.
The closest I can think of to what you were saying is something which counts how many people with Vote-to-close privileges have viewed the post and chosen not to vote to close it, but even that's completely messed up because there are several high-rep users who don't use the review queues, and people with <3k rep can cast helpful flags.
So I'm sorry, but the only option I see is getting a bit more familiar with the homework policy. It doesn't take too long :) Or once you have the 3k rep privileges, you'll be able to see if there are any pending close/reopen votes on a post.