1) Generally good to train after a meal, but long enough so that the meal is digesting. The alternative to that is to train before breakfast, but have a fast digesting protein shake with carbs about 30 minutes before training, sip something during training, then protein shake afterwards, then breakfast. When I train early morning that is the method I prefer personally.
2) Can do either. I would try doing the same body part both workouts in one day, but making the morning workout all compound lifts--no isolation exercises, and the evening session all isolation stuff for pump, no heavy compound pressing. So it would look something like this:
day 1: AM: chest/shoulder pressing PM: chest/shoulder isolation/pump
day 2: AM: back heavy compounds PM: back isolation/pump (rear delts would go here)
day 3: AM: Legs heavy PM: legs isolation/pump
day 4: REST
day 5: REST or Repeat