A Hoyer is a necessity for transferring in and out of bed, a power chair, or toilet (if that is practical), but very few will work for a car, and a PALS that needs a Hoyer won't have the core control/strength to ride in a car seat. Once he is using a power wheelchair, the PALS will need to be in the power wheelchair, which will be driven using a ramp, kneeling lift, or level entrance into a adapted van, train, bus, streetcar, etc.
I suggest you check out some videos (search for "power wheelchair," etc.) for the "pictures that are worth a thousand words." I'm sure you've seen someone in a power wheelchair. It can go most places outside the home, except for older buildings, steps, etc.
You will need to make sure the power chair eval includes a home eval or at least a video walkthrough. It used to be part of the package, but in these times, not always. Not knowing anything about your home, if it's very small/narrow, it is possible your home may not be compatible with a power chair (1) without modifications or (2) at all. If so, best to find out soon. But remember, as long as the chair fits through doorways (24-26"), transfers can take place in any room, so long as there is room for the Hoyer to travel. So you will want to measure the turning radius of the Hoyer in the largest room.
A shower chair cannot go over the threshold. Sometimes you can build up the floor or have a little ramp, if there's running room for that. The ShowerBuddy has its own track so that's another option. There still has to be some floor space available in front of the shower, and room for the ShowerBuddy to be pushed onto the track. There are diagrams with measurements on the ShowerBuddy site. There is a tub version but most PALS will use showers for warmth, if nothing else. Think how cold you'd be in a bath if you were only half in it, let alone how hard it would be to stay upright without a strong core.
Your dad should be switched to a BiPAP ASAP -- get your clinic on this. BiPAPs allow for much lower air pressure when breathing out, which is critical in ALS, and have other features that CPAPs don't.
There are nasal masks available that are prongs, a kind of cup over the nose, and a nylon parachute over the nose. Most people can find comfort with one or another. cpap.com offers free return insurance on many of its masks and offers a larger selection than most equipment vendors.
Ideally, a PT, OT or nurse at your dad's clinic can become a resource on some of this stuff. Do you have a contact that you can call on?