In 30-ish years of gaming, the only time I've used miniatures is if I'm in a game someone else was running and that GM provided/chose to use them.
- How much say (if any) do the players (as opposed to the DM) have in describing the environment?
As much as they have in describing what a game board - sorry, "battlemat" - looks like. Probably more, since it's easy to ask if there's say, a handhold or a skylight above and adjust their plans accordingly.
- Do you use other visual aids to help the players picture the area (a map, a quick sketch?)
Yes. Player-facing maps and elevations can help establish physical spaces. And I find that players using ToTM tend to think more vertically than those looking at game pieces, too. That is, people moving minis rarely think to ask what's above them, whereas people imagining a hallway/room/valley are more.likely to do so.
- How do you keep track of distances, ranges, and movement?
All descriptions. It's never been an issue. And since almost nobody could stand in one place and tell with precision what's, say, 15 or 20 feet away without measuring it, the descriptions and up being more realistic too.
- Anything else you think is important to know about how you use (or don't use) minis/grid
I get that collecting and painting minis is fun. I buy them and I paint them. But what I want to play a boardgame, I whip out my old HeroQuest set. When I want to play a TTRPG I leave the toys at home.