Get Bob Flexner's books "Understanding Wood Finishing" and "Flexner on FInishing". He also has many articles available online and youtube videos. He also has a "wood finishing 101" (or similar title) that may be more beginner friendly, I haven't seen it. He both knows his stuff and knows how to teach it.

For your holes, wood filler will always be an obvious repair. You either need to blend it in by adding faux grain lines and color variation )I'm sure Flexner's books show how to do this), or making a dutchman from the same wood, which you'll also have to blend in using the same techniques. It's often easier to turn the repairs into a feature rather than a bug by using a contrasting inlay for repair, making the former holes a decorative element.

Watch a few of this guys videos. Find yourself a small piece of solid wood furniture (no mdf/melamine or resin) to refinish, like a small stand or table that has a flat top an some turned legs. Once you can get a respectable finish on that, move on to your good piece.
There are other refinishing vids/channels on YT, but this guy is for real, does it all by hand, no fancy equipment, same techniques as a century ago, and very good fast output of projects, he works out of an antique store.
Casey

Here is a link that might be useful: the english polisher

What a great question. Thank you for asking it.

I hope you also have a good local source for supplies and advice. I was glad to find Old Masters stains at the local Benjamin Moore store. The manager has been very helpful advising products. (sometimes I get other products elsewhere, but still appreciate the recommendations.)

filling holes where pulls used to be is pretty easy. making them look good's hard.

drill out the holes, then glue and use wooden dowels to plug the holes. make sure the dowel has a tight fit. sand the ends smooth 1st. if you're careful you can tap it in flush to the surface. you might have to use your filler if you're not happy. in any case, go to the art store and pick up medium to fine line marker pens, lighter in color than the door face. stipple the plugs with the markers. color to taste.
note, the end grain of the dowels will make the colors much darker. test the markers on scrap ends first.

yep... it's a cheap trick, but you can never have too many.

what you're doing can be a challenge for the pros. this trick will give you the best results for your skill level. any questions just ask. good luck.