First of all, @Kristina100, I can put your mind at ease about the weird-looking email address. That is just the temporary address that Airbnb provides us all so we don't have to give out our real email addresses. It allows you to send a pdf of directions or photos or whatever. It disappears once the stay has ended. I don't often need it here, but it can be handy. So that bit is nothing to do with your guests and any sketchiness.
It would be nice if they would answer you, however. Do ask again, and tell them it is to put your mind at ease.
As to providing proof that they have booked, if you have asked them that, then it is they who will be worried. It is Airbnb who provides you proof of booking, not the guest. Take a look at your dashboard to see whether you have a confirmed reservation.
It will be a good idea to get to know the Airbnb site and policies really well moving forward. You won't regret the time it takes. All the best!