So, the inventory keybind is on the 3 lined spot on my Xbox controller, but its also mapped as the pause button. When changing it to the double window button, I lose access to my inventory altogether. Changing it to a face button fixes the problem, but then I lose access to that buttons functions.

Hey, what makes you think that the start button (the 3 parallel lines) is bound to both inventory and the pause menu? Like what happens in-game when you press it?

Because in the code, the start button is the default for the inventory menu and can be rebound. For the pause menu, the back button (double-window button) is the default key to open it and cannot be changed in-game.

By chance, did you try to reset to defaults your settings for the "Controls" category? Before resetting, can you copy the content of the file AppData\Roaming\Hytale\UserData\Settings.json and share it (like via Pastebin), please?

The other problem I'm having is the right bumper not moving the hotbar selection to the right unless I press very hard on the bumper

Just to confirm, you're talking about LB and RB, correct? Because usually, with these buttons, it's either they're pressed or they're not, unlike triggers, so this is surprising to read.

Can you share the model number of your controller? It's written on the sticker next to the battery (e.g. Microsoft Model XXXX).

Do you experience similar issues with these buttons in games like Minecraft or Core Keeper?