Those are some of the problems I have encountered and solutions which work for me.
P: Water is scarce.
S: Brush, spit (profusely), rinse, spit, rinse, spit. This amounts to only 2 small gulps of water - as little as 100ml.
The brush shake hard, rinse lightly, shake hard. That gets the toothpaste residue off.
author: @Chris H
P: Batteries are scarce and in the dark the toothpaste drops to the ground.
S: Squirt the toothpaste into your mouth instead of onto the toothbrush. Soon you will learn to measure the correct dose. And will obviously never drop it.
P: A toothpaste weighs a ton.
S: Purchase a tiny package or carry a nearly empty one.
P: I forgot my brush. And paste.
S: Chew some tough grass or young branch to make it into a brush. Use it to remove food in between the teeth. Never forget again as 10 days without tooth care is too much.
P: My brush is wet, it's gonna rot.
S: Dry it at the rest/dry/eat session at lunch.