Without my codex to hand, I can't remember 1), but:
2)No, the section on Grenades in the main rulebook explicity states that the benefits apply to the model, not the unit.
3) No, they may not assault a different unit to one they shot at. The special rules relating to shooting for MCs are that they can fire two guns, and that they have "Relentless", ie can make usual movement and charges even if the gun(s) they fired were Heavy or Rapid Fire.
4) No, one rider can only shoot with one weapon. A Space Marine Attack Bike is allowed to shoot with two guns, but that's because it has a rider and passenger.
You are free to choose whichever gun you want to fire: in the case of Splinter rifle or pistol, the rifle is better, as bikes also have Relentless, so they have no limitation to their movement despite the rifle being Rapid Fire.