These things could be achieved as per the methods used in standard mt32-pi hardware builds, i.e. connecting directly to the Pi's GPIO pin array. How you physically access and connect to the necessary pins can be decided by you.

2. The buttons can be connected to the appropriate pins of the Pi as shown at the link for mt32-pi's control surface. Each of the (currently 2 supported) buttons can be connected to it's own particular GPIO pin as shown in the link, with it's other wire connected to a spare Ground pin that you choose from the Pi's array of choices.

The optional Rotary Encoder (or 'volume knob') has it's own wiring scheme as also shown in the link.

3. The ClumsyMIDI bill of materials refers to it's screen header as:

I assume you can attach one of the screen types supported by mt32-pi directly to the Pi's appropriate pins as described in <--the link, and edit the .cfg as shown.

I further assume with fair confidence that the ClumsyMIDI's own screen connector is simply passing through that relevant set of 4 pins relating to I2C screen connection, from the Pi, without custom alteration - and that you could therefore utilise those pins directly to connect another 5V compatible I2C screen, as you have suggested - but cannot say with absolute authority, not having a ClumsyMIDI myself to test or inspect.