@Miriam554 First of all, you need to understand the difference between an Inquiry and Booking Request. I say that because you have used the terms interchangably here. For an Inquiry, you have 3 choices- pre-approve, decline, or just message back. Just messaging back on an Inquiry stops the 24 hour clock from ticking (altho you will get pesky notices from Airbnb urging you to pre-approve, but you can safely ignore those). So if a guest has written something that makes you uneasy, or that indicates they haven't bothered to read through all your listing info, you can just message back, explaining why your place isn't suitable for their needs, or if it's just a matter of insufficient info, ask them more questions. Most of my guests have sent nice, informative mesages right off the bat, and I just go ahead and pre-approve those (which doesn't necessarily mean they'll go on to book). If they just send a message like "Arriving about noon" when I haven't even pre-approved yet, I'll prod them a bit and that usually leads to a more forthcoming message. I might say something like "Hi XX, thanks for your interest in booking with me. I just want to ensure you have read everything on my listing and are aware that....." A lot of people these days are just used to sending quick text messages and don't really think about the fact that as hosts, we want to know a bit about the people who are asking to book our homes.
If it's a Booking Request, you do have to either accept or decline within 24 hours, but you can still message with the guest before then if you'd like more info or to make them aware of things it seems like they didn't bother to read. If they are non-responsive, or they still make you uncomfortable, just decline the request before the 24 hours are up.
As you said, most guests are great, so it's a matter of learning how to deal with the ones we have doubts about. I have had many guests with no or few previous reviews, or who have just joined, and all but one have been fine as well, but you may need to make sure they have read through your listing description and understand what they are booking, as well as re-iterate your house rules and expectations re respecting the space and cleaning up after themselves. And when they arrive, make sure to tell them that if they are unsure about how to work something, to ask you, rather than use it improperly and break it, and if they damage anything, that hosts appreciate it when the guest lets them know rght away. Accidents do happen, but we are usually much more willing to chalk it up to normal wear and tear if the guest fesses up, rather than hiding it or not mentioning it and just walking away. As for the messy guests, well, some people are just messy. I've found it evens out and the ones who leave it clean and tidy are more common than the ones who leave it a pigsty. It's just part of hosting to accept that sometimes you'll have a heavier cleaning job, or have a few items stained beyond salvaging.
Of course if they do major expensive damage, they should be charged for that.