If you are purchasing your home with a CHFA loan, you may rent out a room, as long as you reside there as your primary residence. The potential income you may or may not produce from this rental will not be considered when qualifying for the mortgage.
Hope this helps & good luck with your new home search!
I think the answer is yes, you can. I don't think there are any restrictions on having a room mate, but you should check with your loan officer to be certain. I don't think you will be able to count any of the rental income when qualifying for the loan.