Facts below:
One tenant is on Month-2-Month and the other just started a short term lease. Both with the current owner.
Are you sure it's a short term lease? I was pretty sure CMHA requires 1-year leases but I could be wrong about that. See if you can get all the CMHA paperwork from the seller to confirm.
Can i ask the seller to collect the May rent and entirely credit it to me on closure?
Probably not the best way to handle. What should happen is the seller should contact CMHA - email Shay Mock (you can look up her email or phone on their website) and request the May payment to be held due to an upcoming sale. That way they won't release it the seller, and you should be able to collect it directly once you get set up.
I intend to keep my tenants and sign long term leases, but is CHMA going to need a new inspection because the title change?
No they will not. However they do still do annual inspections (though they are on hold right now due to coronavirus and they're allow self-inspections).
I have not spoken to any tenant yet, but how do you suggest I do this? Speak to them and figure out if they are committed to stay in the first place?...
I don't think you really need to speak to the tenants just yet. You're going to need to get set up with CMHA regardless to collect May and June rents. I would wait until that's all done before discussing the tenant's future plans with them.
Anything else I should watch out for?
Section 8 is no golden ticket, even now. Section 8 tenants beat up on properties badly, and their financial situation can change at any time so that they start to become responsible for a portion of the rent.