@Joan2523 You are right to be wary. And no, month long bookings are not okay, altho some hosts manage to do them successfully. You don't want guests to stay long enough to gain tenancy rights, as there is no protection from Airbnb, and the Airbnb so-called security deposit is bogus.
However, aside from that, I have had guests who showed as members for several years, yet had no reviews. In all cases, it turned out to be totally innocent, when I said I was curious about that. One guest had had 2 previous stays, but her hosts hadn't bothered to review, one had joined planning a trip, but work committments got in the way, the other had stayed in Airbnbs with her husband, booked through his account, but she liked perusing listings around the world, like you'd read a travel magazine.
All if these guests communicated well with me, I acccepted their bookings, and they were all great guests. But it's definitely something you can ask about and and shy away from if you get a weird feeling.
For a guest who asks to stay a month or more, if you might be open to it, you could suggest they book for a week or two first, to make sure the place is a good fit for them and for you, and then rent to them privately after that, with a real legal agreement (don't mention this in Airbnb messaging, though).
But you have to decide if you want to be a lnlord or a host, as those are two different things.