That's fair. Perhaps another style of DMing and/or a different system are more your speed.
If you actually have to use that much math more than once in a blue moon, you're doing it wrong.
There's no grid in the sky, though
You absolutely do not have to RP this. You can say "No." You can say "Ok, you go off and do that, what's everyone else doing?"
What's his deal?
Starbucks is a real coffee chain that exists in the real world. Moondeer and sunfawn follow the same naming scheme, but the players didn't realize that was what the DM was building to until the big reveal. It's...pun-adjacent.
Queercoding villains to make them seem dangerous and deviant to the people of the time (and those that are still stuck in that time). Admittedly, the people making that decision probably weren't conscious of that being why they thought eyeliner made him look villainous.
Peckromancer
You select the level of abstraction for different things based on what is and isn't the most fun to delve into. If your group enjoys poking every surface with a 10 foot pole, it's not wrong to play with that level of granularity. It's just that all the interesting things you can do with a 10 foot pole are pretty mined-out after 50 years so we tend to direct our attention elsewhere.
In 3.5 at least, if you're in a space that isn't big enough for you to change size, RAW you just...don't.
I just feel bad for the loincloth mimic.
I believe that's how it's handled in D&D too, or at least how my table has always done it. I meant more as a practical matter, you're very unlikely to have a vertical wall grid and some kind of stand of the correct height for your minis, so you can't just count squares like you would for horizontal movement. That's when the Pythagorean Theorem comes up in my experience.