@ai6yr
Then, as now, manufacturers copied each others styles. My guess is John Keal dining chairs for Brown Saltman. Curved back bar. Stretcher bars between legs for stabilization. Mild curve to the taper of the legs. The back cushion has a smile on top and bottom, like a happy calzone.
This should be an easy reupholstery job. mostly glued solid wood frame. If yours has knobs on the back, those may cover screws.
Do any wood restoration first.
@ai6yr
Your choice, since you live with animals.
I used oilcloth for my kitchen chairs, and strong cotton fabric for the ones at the table away from the kitchen.
The oilcloth stands up to regular wipedowns, and collects fewer cat hairs.
The cotton on the other seats can be removed, washed and reinstalled every couple of years.
If I were more grand, I would buy mohair velvet.
I use my canvas pliers for upholstery, because I have some. They provide a more even spread of the fabric as you staple. Regular pliers work too.