@Marguerite22
As long as the guest is extending via the Airbnb booking system, then the calendar will be blocked to other guests, just like with any other booking. For long term bookings, Airbnb collects from the guest/pays you monthly. Be aware though, if the guest's payment method fails and Airbnb is unable to collect from them, you might be in a sticky situation.
That has never happened to me and I have hosted many long term guests. However, I do try to vet them carefully before accepting a booking.
What is most important though (as others have mentioned) is that you are aware of your local laws. At what point would these guests gain tenants' rights. If they would gain them, then you need a proper contract and security deposit rather than relying on Airbnb to help you should anything go wrong. Although you might have had good experiences with this in the past (I also prefer hosting long term Airbnb guests to regular long term tenants), Airbnb customer service is patchy and best and getting worse and worse. Just read some of the horror stories posted every day on this community centre. There is no guarantee that you will get fully, or even partially reimbursed for damages. If your guest ends up being a squatter, or otherwise problematic, Airbnb are not going to be coming to your door to evict that guest. You will be left to deal with the situation yourself if the guest refuses to leave.
Also, there may be legal limits to how many nights you can host on Airbnb. Have you checked these? In London, if you are renting out an entire unit as an STR, you are only allowed to do so for maximum 90 nights a year in total (across all stays). There may be a similar law in NY, so do check this out.