1: I've heard of DACA beneficiaries getting mortgages through credit unions without any issues. There were topics here on the forum in the past about discussing mortgages. I'd recommend hitting up multiple CUs in a short period of time when it's time to get your pre-approval, so all the inquiries will only count as one on your credit report. Then, based on what the requirements are at the different places, choose the one that's the easiest to get.
Or go to a mortgage broker, and let them do the work

2: If they're only co-signers, and they're not on the title, there's nothing really they can do. If you put them on the title, they become co-borrowers and get ownership rights