You can do all of the things you want and most should be pretty straight forward.
I use my Win tablet to control MC, I use MC's native functionality for most things but also use remote session software (Team Viewer)
iOS and Androis apps work great but they are limited in functionality.
Room correction you have 2 choices the simplified "Room Correction" in DSP or "Convolution" which is for advanced room correction.
Tone control you have choices here too: Effects, EQ and Parametric EQ.
Fast Access?
Presets are easy enough especially with the
AutoEQ plug-in which allows you to select which preset you want to use for every song.
Best output formats are ASIO if supported or WASAPI.
Did you try split in both Columns and Rows, I find Rows works better for me.
Can't speculate on the DSP from remote location as I have never tried and my wife has my Tablet.
Edit: If you need help with anything specific don't hesitate to ask there are many great people here with a plethora of knowledge.