Broker may know of loan companies you are not familiar with, but they will be expensive. Try small local banks. Also, consider asking seller to hold paper. They potentially save on taxes by reporting sale over a number of years. For the down payment, savings, life insurance loan, home equity loan, 401k loan, etc.

Most ITIN holders don’t have authorization (green card) to work. Curious, did you tell them they are ITINs, or did their validation reveal that?

It doesn’t. I use a personal account for one of my businesses. It is separate from my actual personal account. This used to save me alot of fees. There’s a few banks that have low or no fee accounts: PNC, Chase and a few local ones.