I had a couple in the 80's and 90's when I had far less area to mow than I do these days. I never had any issues with the models I had back then and unless they hit a serious brain fart I can't imagine they will have regressed with their new designs. Mine had spacers to adjust cut height. I don't see the hover models as any more of a danger to toes than a wheeled model. Both will equally amputate if you give them the chance. I found the easiest way to cut slopes was to do it from the top down, start at the top and allow gravity to take the mower down then pull it back up, don't try pushing uphill. I used a mowing action similarly to how one would use a vacuum cleaner, but then I did have considerably less to cut back then. As long as you go over everything you end up with a nice level lawn As for controlability choose a model that's a suitable size for your mother to handle. From my recollections of the models I had Pros. No wheel groves and you can cut in any direction, so corners and recesses are easier to manage, no having to go backwards then forwards to cut the strip next to the bit you just cut. Very handy if you have lots of obstacles in your garden, much easier to mow around things. They were electric so no engine maintenance, starting problems, fuel cans, oil or air filters to worry about. Just keeping the housing clean after cuts and blade service. Not suggesting that the motors last forever. Cons. It was electric and you had to keep moving the extension cords out of the way. Not being restrained by wheels the free flowing movement means you have to be way more aware of where the cord is. As far as cuts go they did just as good a job as any wheeled rotary mower. There are no wheels, so you have to carry it back to wherever you store it, bear this in mind when you choose a model size for your mother. I cannot comment on the reliability of today's models or the suitability of a rotary mower for the kind of grass you have, all I can do is pass on a consumer review.

....but did not remove the gas.... Your carb is probably gummed/varnished up, or else you forgot to turn on the fuel shut off valve. You need to read the OM regarding storage.

Thanks for the comment. Yes, it is a self-propelled Troy-bilt (circa 1994) with an 8.5 HP motor. Perhaps you're right. Unfortunately, I gave up and brought it to a mower repair company. When I get it back, which could take a while as this is their busy season, I'll post their findings. I can't figure out how I was able to drive the mower to the garage to change the belt. When I checked the belt before driving it, the belt was broken, more off than on the pulleys. After I got to the garage, I then removed the old belt. Never having changed a V belt before, I tried to pull on the broken belt, and probably pulled way too hard, given the resistance. I finally figured out how to move the guides on the engine pulley, which were difficult to see and get to, and then completely removed the belt. I may have tampered with some moving part, however, with all the pulling I did. Hopefully, the repair man will give me an honest accounting of the problem.

Literally crawl all over the tractor looking for numbers. Many of the clones use a number of a similar format to their siblings. That may help identify the tractor. Other things, such as engine Brand Model, type/spec and transmission type/speeds can also be helpful.