Yeah I would say you probably need a Mega to do what you want. Counting all the buttons and LEDs on your drawing you're close to running out of pins on a smaller Arduino, there are ways to expand the number of inputs/outputs using additional chips but these days it's often easier just to switch to a more powerful processor. I don't think you need to worry about running out of memory, you're not trying to do anything particularly complicated, it's just reading some switches, turning some LEDs on and off and sending the MIDI data, pretty easy stuff for the Arduino.
To answer your question about the screens, the big one just needs power and a suitable video cable back to the PC that is running the Mobius software. How exactly you do this depends on the screen that you buy and what video ports you use. I'm not sure about the smaller one, the big one looks like it is just duplicating the Mobius GUI that would be displayed on the PC but do we know what the little one is displaying?