Can someone tell me what:
masterkeyboard
It's like the keyboard on a digital piano or synth. But, just the keyboard, none of the stuff that makes a noise. It generates midi and you can use it to control a bunch of synths and modules that make the sound.
Most master keyboards have more sliders and buttons though, so you can assign them to different midi controllers.
That said, you can use a synth as a master keyboard - so it's possible that it has its own built-in sounds too.
aftertouch
Aftertouch sensors are are either per-note, or on some there's a single strip across the whole keyboard. They detect if you press harder on a note that is already held down.
Pressing on a held note will generates a midi controller value. That value is typically used to add vibrato and stuff like that to samples that can vary the sound after a note is played. Obviously not much use for a realistic piano, but for brass instruments, where you can vary the pressure / timbre of a note that's playing, it helps you create a more realistic instrument sound.
half pedal functions
In piano terms, half-pedalling is using the damper pedal but not pressing it all the way down to get varying sustain effects.
In midi terms, most midi damper pedals generate on / off - either the damper is up or not.
A pedal with 1/2-pedalling will generate a variable value between 0-127. This is used [to a greater or lesser extent] to recreate the effect on a real piano if you don't press the damper pedal down completely so that the dampers are still in contact with each string, but not completely damping it.
Most implementations don't use the full 0-127 range though. They'll have a smaller number of levels between 'dampers completely on' to 'dampers completely off' for which they'll generate increasing levels of sustain.
Topic: masterkeyboard with aftertouch