What is the best advice for a non-ambulatory 82-year-old?

With respect to the wheelchair vehicle, there are a lot of variables. My mother used to use an electric scooter. She had a minivan with the rear seat removed, and an automated lift with an arm that picked up the scooter, lifted it and swung into the back of the car. It was powered through the car's 12v socket. She never used that because she needed someone else there to guide the scooter and lower it in the proper spot.

Then she got a hitch-mounted pneumatic lift on the back of the van. She couldn't really master the mechanics of that either and eventually it got removed and discarded. Now we use a folding transport wheelchair that folds up and fits behind the folded rear seat in the van. It's really more convenient all around.

When I take her grocery shopping, I get a motorized cart from the store and drive it to the car and she uses that. For medical appointments or other designations that don't provide motorized carts, I push the wheelchair. A side benefit of the push wheelchair is that you can bring it right up to the table in a restaurant and she can sit in it to eat. A motorized scooter doesn't allow that - she'd have to find a place to stash it and transfer to a restaurant chair.

I'd advise anyone to start with a folding transport chair and see if it meets your needs before investing in a power chair or scooter or expensive renovations to your car. Oh, and in case you don't know this, the transport chair has four small wheels, and can't be manually rolled by the person sitting in it. The ones with the big rear wheels allow a person with upper body mobility to wheel themselves around, but they're much heavier to lift in and out of a car. Something to consider.

All of the things you listed, hospital bed, wheel chair, and lift should be covered by Medicare with a doctor's order. Talk to your dad's Doctor about medical necessary durable medical equipment and work with an approved Medicare equipment provider (or Medicare will not pay them.) Get to know whether you need a hoyer lift bag or a get-up-lift (invacare) for your dad. Determine if your dad needs a custom made wheel chair, or an electric motorized chair. Also, if you need a fully functional hospital bed Medicare will only pay for part of the total cost.