Shrimp can indeed be eaten by bettas so I wouldn't recommend it unless you try it out with ghost shrimp before pricier cherry shrimp (I'm assuming you want cherry shrimp?). I've kept bettas with shrimp but I've also seen bettas eat shrimp.
I find divided tanks to be annoying so I'm no help with dividers. If it was me, I'd go for a single male. Some of them are absolutely stunning and look amazing as the main or only fish.
There's a sticky in this forum on cycling with a bit of live plant info. Check it out and let me know if you still have questions on those topics.
Yes, adding fish to a previously shrimp-only set-up will increase the amount of maintenance. But bettas are easy to care for and not messy at all so it wouldn't be a significant difference, especially with live plants.
So are you looking for more 10-gallon suggestions? If you don't like guppies I don't see why they're on your list
. Look into harlequin rasboras, celestial danios, cherry barbs, white cloud minnows, and pristella tetras. All of those (and it's not a comprehensive list by any means, just some ideas) are easy even for beginners, hardy, social (can live in groups), won't mess with plants, and won't eat shrimp. They'll all thrive in a peaceful, small, planted aquarium.