You can hide the number pad from the keys. Or hide the keys entirely. Or keep them and customize which functions they activate, including custom user-defined functions.
could I keep only half of all the keys (e.g., I'd never need 0-9 or cursor keys, but then maybe ANS is useful), reoder them and attach a shortcut to each button?
Or replacing sin with the rad/degree switcher (without the dropdown)?
Yes, you can hide all the 0-9 keys. And add rad/degree buttons. And set whatever functions/settings you can have elsewhere in the UI as buttons. And add or remove columns/rows from the "keypad". The upper-left button in the custom keypad will always be to edit the custom keypad itself, otherwise it's fully modifiable by the user.