@Valerie283
It is fully possible to have any kind of photo on your profile. Add to your house rules that ID must match profile photo, then ask guest to upload. Make sure you accept or decline within the given time frame or your response rate will take a hit and your calendar may be blocked for the dates in question.
Anyone can send a request - they do not even have to be verified. If you have Instant Book enabled and receive a request, it can be an indication that they do not meet your booking requirements. It is then up to you in communication with your prospective guest to get the party going. If they are unwilling to co-operate, I would decline.
I have a recent booking gone through from a verified guest where there is no photo whatsoever - their location is wrong too - they are Germans.
https://www.airbnb.com/users/show/167192451