I'm looking for advice on a good floor plan

I used an online tool when I was arranging the furniture in my living room- something like this http://opunplanner.com/interior-design-software.php you can play around with the space and your specific measurements to get great options before having to drag the furniture around again and again. Have fun!!

You can get a Queen size Murphy Bed that uses a regular mattress and some of them have shelves on each side. You could probably find plans to build one if you are handy.

I'd suggest coating the floor with a water repellent blocking paint first, then install vinyl flooring that looks like hardwood. It's flexible and easy on the feet. Area rugs will be a welcome addition also.

Appliances will have to be placed near proper electrical outlets. Hopefully the bed can be positioned near a window for egress purposes. Think safety first. Best of luck.

I'd put the appliances on the back wall and make that the kitchen area with cabinets above and beside the stove, refrigerator. Install the microwave above the stove. In other words, make a separate space for the kitchen area and have the hood vent to the outside. If there's room, you could have a small island with room for a bar stool so she has somewhere to eat.

I'd put the bed on the opposite wall and build a closet on the side wall. On either side of the bed could be small dressers to hold smaller clothing items (underwear, socks, etc.) and double as night stands. If you're tight on room , just use one.

A small side chair or recliner could go on the wall opposite the closet.

check with a contractor/ or city for area codes re: garage conversions before you begin. some will permit it, some don't. some will have you put your utilities on a separate meter. that's what happened at my place. 1/2 of a former 2 car garage was made into office space - 1st for a small animal vet, then tax prep, then furniture restoration, and now my craft room.