Learning square names and colors isn't something people try to do, it's just after tournament games (where you're required to record moves) and studying it just automatically happens. For example you attack f7 so many times you just remember right where it is and that it's white... or maybe you play the KIA and you know the h1-a8 diagonal is white.
Practicing these things on their own shouldn't increase your rating at all.
I improved by playing slow games with opponents stronger than me, doing tactic puzzles, and reading books. Listening to others that seems to be the way to do it. I played blitz every day for years, but that sort of thing just built bad habits. Not that speed games are completely bad, but they're not really going to help you improve.
The time frame for a few hundred points is more usually counted in years. True it's easier the lower your rating is, but it's not something to focus on. Instead the focus should be what can you learn from your games, and the mistakes worth learning from happen in long games where you play seriously. Compare to mistakes in blitz where it's usually "I was low on time so I made a risky move that didn't work out."
I've been stuck between:
bullet: 950ish
Blitz: 1200ish
standard: 1450ish
I've done some tactic training via the site, some mentoring as well, and computer analysis.
I do not write down moves (should I?)
I can't point to a random square and tell you the square notation (should I be trying to learn that?)
If I begin doing these 2 things, do you think my rating will rise? how much? time frame?
What other things should I work on to bump it up a few hundred points over a few months?
I usually play 10-20 bullet or blitz games per day, I play standard games online infrequently, but I do play long, untimed, games in person several times/week. they usually last 2-3 hours total time.