I'm sketchy of the idea of rewriting and resubmitting a review. Would resubmitting a review mean to delete the review, rewrite it and wait for it to be accepted or is it just changing the parts needing changing and just click the little 'Submit' button? Or is it entirely different?

No need to delete it. I've resubmitted a couple of reviews before; both times I did exactly that, made the changes I wanted (one time it was as minimal as changing Freddy Lin to Freddy Lim at his request) and pressed submit again. I get the idea that the submit button fires it back into the queue whatever you've done with it. Then it's just a case of waiting for it to be accepted again.

sushiman is correct. That's exactly how it works.

I haven't done this yet, but if you do resubmit a review, do you lose points and gain them as if it never existed previously?

I've seen that question asked a few times. If I recall, you are not supposed to gain/lose points but if the acceptor is not paying attention you will get the standard points for an accepted review.

You won't lose points (mechanically) when you actually resubmit the edit. Edits are not supposed to receive any new points (the menu we use has an entry something like "0 points - edit of old review"), but occasionally they do, on account of mod error. If this should happen to you, don't worry about it. It won't be seen as underhanded on your part.

Yeah, sometimes people get all self-righteous about not wanting to accept these "unearned" points, but frankly we'd prefer you just keep them and not bother an admin with it. Admins have better things to do.

I just completely re-wrote my review for Soul of a New Machine and there were no dramas whatsoever.