Basically, there are two types of toy requests here on EF. (There are more, but you'll deal with those more as you become more advanced.) The two basic ones are manufactured sponsored and Eden Fantasys sponsored. The EdenFantasys sponsored one is the one where you can pick off of any product on the site that has less than two reviews. The manufactured sponsored ones are the ones where manufacturers give specific toys out to review.
EF-sponsored reviews can be done once a month. I think it goes from the date that you have actually *requested* the toy and been approved - not when you submit the review. Once every month, you can request any product, in your price range, that has less than two reviews.
However, manufactured reviews can be done anytime - they are first-come, first-serve, so anyone can take them. You can do unlimited manufactured reviews per month, but products are usually limited.
You can only review one toy at a time basically. Again, advanced levels have different systems to get involved with, but at the basic levels, just one at a time.
If you chose an EdenFantasys sponsored review, you have to wait a full month before requesting another one - don't worry - the system won't let you request one until you're done with your full month. If it was manufactured sponsored, you'll be able to request another product as soon as you submit your review.
You don't have to wait so long to write a review, but it's preferred if you've used the toys at least a couple times before you choose to write the review on it. Reviews are due back in 3 (maybe 4 - not sure) weeks after they've been assigned, so that gives you plenty of time. You want to write a good quality review since your ranking is directly connected to the quality of your reviews.
If you still have questions, I tried to write up a write-up on my blog for beginners to answer beginner questions: