As for the look of those buttons and where to put them, not sure if my suggestion is good, but how about having them floating as a row at the bottom of the screen, and right above the keyboard when it's active. This is sort of how it looks like in `Simpletask` (another task app on F-Droid that I tried out and liked).
If you toggle on 'Look and feel > Back button saves task' then you can use your back button instead of the save button up in the corner
I can see some really nice shortcuts that must make it very quick and easy to use once you're used to it, but take a little learning.
(I'm not affiliated with them, I just use and like their app)
They even have a web interface to the same lists: https://www.ourgroceries.com/overview
Edit: I think I get it now, you prefer to not have the online component at all.
Two small improvements I would suggest:
1. A sorting order where checked tasks are moved at the bottom, keeping only the unchecked ones on top. (I could not find this if it's already implemented). Note: I want to see all of them, just have the checked ones moved.
2. The save button on task creation is a bit weird. It occupies the top row, together with the delete button on existing tasks, but the checked button is floating on the right. You might want to unify the look of these 3 buttons.
Otherwise, good work! I'll be using it from now on. Normally I'd use Orgzly for tasks, but grocery lists are a bit different, you want to be able to operate them with one hand while carrying your groceries with another. This app allows that while Orgzly is a pain to work with as it requires multiple actions to mark a task done. I know this from personal experience.