The small holes are probably what you suspect, staple or tack holes. For upholstering, if you think you'll need pics for guidance, I'm working on a similar project now. The wood in/of the groove appears to still be solid (not too pitted by the staple/tack holes), but I can't see exactly all what's there, the condition. If there are some areas that are "chewed up", fill the areas with epoxy or some good filler in those places, i.e., repair the wood if need be.
Guessing - Conservatively, it'll take a yard and a half of fabric for upholstery. 27"L X 30"W for the seat; 20"L X 18"W for two backrest panels.
Before you start your reupholstering, clean up, repair the chair frame (loose joints), if need be, and refinish the woodwork.
That groove space is for attaching your new upholstery.
1) First, one fabric panel will be attached facing to the back.
2) Next you'll attach a thin layer of padding.
3) Next you'll attach a firm support - a sheet of somewhat heavy cloth, burlap, or some other firm support. You don't want to depend on your fabric for backrest support, so you need to install something with a little more beef.
4) Next you'll install a good/reasonable amount of padding (to your liking). You decide the amount of padding (puffiness of the backrest cushion). Don't over due the padding. You don't want a balloon effect (that kind/amount of puffiness) for that style of chair.
5) Next, you'll install the other fabric panel facing forward.
6) Next you'll install a trim feature - gimp, double cording or decorative nails. Gimp may be easiest if you've never upholstered before.
Is the seat a board to be upholstered? Or is the board for the seat missing? If missing, you'll need to cut a new board. Or the seat support may be of another application (springs or jute webbing support?). I suspect a board support.... Those corner triangle braces on the inside of the seat frame may be for a seat board. Do those corner braces have a screw hole in them, for securing a board seat support? I can't see exactly what is there.
The above is a start.