Is higher Hz and higher samples always more accurate?
Basically yes. There has been little problems with 8 kHz sampling, where you can see random spikes at random times. It might be just fine for hours or screw your whole setup. I would stay at 4 kHz and lower, if possible.
Does it shorten battery life?
I would guess that it depends on how long it takes to take those samples, so lowest Hz and highest samples would use more energy than max Hz and lowest samples. Shorter logging interval drains batteries faster, but you should get several days in any case.
After initial tests …
Which firmware/app versions do you have? There was a bug that made 10 minute intervals unusable and generated 10.176 second intervals instead. That should have been fixed a long time ago, but as most of us at this forum use beta-app, its hard to say what you really get from app/play-stores outside beta program.