midi-keyboard controlled learing / practice / compose program on linux

hi.
i'm looking for a linux program that would ideally (i
do realize i may be dreaming) allow to

1) interact with the program using the midi keyboard,
not needing the computer's monitor right beside the
midi keyboard
2) learn piano & rate me how well am i doing (how many
notes i miss / get timing way off)
3) record (multi-track) / rewind / replay / edit my
musical ideas

explanations:
1) the thing is that lugging the piano to the monitor
or the monitor to the piano is quite impractical, and
i can't keep the piano with the monitor, plus having
to work at the same time with both the piano's keys
and computer keyboard keys / mouse can be quite
awkward.

2) it would be great to have some software that can
try to teach some theory (see "PS" below) and rate how
well am i practicing. also something that would allow
e.g. left / right / left+right hand grading, you can
set own tempo, rewind, fast forward / back.

3) it would be nice to create and edit a multi-track
recording right from the piano keyboard, i.e. quickly
rewind, slow down, speed up, FF, change instrument,
delete notes, move them back/ahead, mute track(s),