A few thoughts:
I'd give serious consideration to having him rent instead of buy, especially if his health is poor. Owning a home is good in the long term, but in the short term the transaction costs of buying and selling (realtors, appraisals, title/escrow, mortgage fees, etc.) can outweigh the benefits.
It's also possible that his needs for where he lives might change. He may need to move into some sort of care facility, retirement home, skilled nursing, etc. And he might need the equity from his existing rural home to help pay for either his care or his entry fees into such places.
But yes, he may be able to get a mortgage based on his RMD's. It's probably better to set up his RMD's as a monthly amount of RMD/12. Banks love to see monthly income, and they generally consider RMDs income even though technically they're not.
As far as your last paragraph, beneficiaries on everything you can is an excellent start. Check what your state allows - you may be able to add beneficiaries or use TOD/POD designations on his taxable account if he has one, his bank accounts (checking/saving), and possibly his house and car if applicable. These designations are nice because the transfer can usually happen with just a copy of the death certificate instead of waiting for probate.
The other general thing to do is for you to make sure you're aware of all of his assets - at least the institution, contact phone, and rough amount. If his memory or mental ability is declining, it would be a shame to lose track of any assets due to just losing track of them. If your relationship allows, try to have a discussion with him to go over that stuff sooner rather than later.
Finally, you should also talk with him about his medical care wishes. Does he have someone he wants to make decisions for him? Does he want a DNR? States differ in how they implement this stuff, so this may involve durable health care POA, living will, health care directives, POST (physician order for scope of treatment), or other such terms.
