Multi-emitter transistor: does the transistor turn on per-emitter or as a whole?
if there's a base current through emitter E1, does this result in
  collector current through just E1 or through both E1 and E2?


Just think what would happen in an AND gate if both emitters received current when only one was taken low: -



Imagine input A is low and input B is high. Input A takes current because it is low and if that caused input B to fall to 0 volts then the signal driving input B is being corrupted by that action.