Hey El, It won't be the same as all eq's are different, though theoretically if you had the same centre feq, slope and bandwidth (i.e. parametric eq) it should come close.
a) you should get close/similar (depends on slope and bandwidth of each eg (and also the eq filter design, lots of variables here...))
b) as above but probably not, though should be similar (all eqs sound different (for many reasons see attached)
A fundamental of recording is capture the sound as faithfully, cleanly and best as possible and only use post eq if you "HAVE" to. If you want to use eq as a FX, you can, in your case IMO it's better done in MP1 / Rane, you are then creating the sound you want to record, and then record that as faithfully as you can.
Another driver here is the eq in MP1 and Rane is analogue, eq in DAW is digital, the attached pdf will help your understanding analogue eq vs digital. You have to spend serious $'s to get a digital eq anywhere near as good as a really good analogue eq (typically they need very wide back plane processing (128bit or wider, the majority dont) to not wreck the signal , check out Bob Katz site, (Mastering Engineer) he had a good discussion on why).