@William1809
Well, you can't prevent people from lying when they are booking. I don't have the problems you do because I have an entirely different type of listing, but the way I see it is you can do a few things.
1. If you use instant book, turn it off if you feel you can do this without suffering too much in the search rankings.
2. Try to spot red flags. This means communicating with your guests and asking them questions as much as is reasonable to do so. Sometimes guests will inadvertently give themselves away but not always in the first message. I also ask guests to confirm they have read the full house rules (I have an Easter egg question they need to answer) and to confirm they understand specific points, which in your case would be no parties and no extra visitors. 3. If you have charges based on the number of guests, remind them of this (also include it in your house rules) and of the security camera. Don't mention the camera in the context that it's there to check up on them, but rather, "Just a reminder that there is an external camera there for your security." This will still get the point across that they can't just bring in extra people. You might want to mention in your rules not to tamper with the camera if that is something you've experienced guests doing.
4. You have the correct info in your house rules, e.g. no parties/events, no extra guests, noise level, disturbance to neighbours, but not all guests read the full rules. Make sure they have done so (see above) but I think it's also worth mentioning some of these points in the listing description itself, under other things to note and also 'you must acknowledge'.
5. It might also be worth mentioning something about guests being responsible for paying for damage or extra cleaning. It's great that your guest was upfront about the mattresses, but you really don't need this sort of thing happening. What if you had new guests checking in before you were able to replace them? Also, not all guests are going to be that honest about it.
6. Get your own additional insurance anyway. You will see from many other posts on the CC that Airbnb does not always pay out for damages and, also, they could even suspend your listing if they think a party has happened there, especially if there have been complaints from neighbours.
7. If you are able to do an in person check in, I would advise you do that whenever possible.