no, cars that get started to be moved about a parking lot and then stopped regularly have re-start problems because the spark plugs foul. and cars that just do short trips don't get their oil hot enough to evaporate start-up condensation.
won't happen. the injectors are sealed.
see above - injection systems aren't open to atmosphere like carbs.
bottom line, 3 months is trivial. as tegger says, change the oil, install a smart* charger, inflate the tires, and walk away. it'll start right up when you get back.
- a "smart" charger is essential. the old fashioned "dumb" ones, i.e. ones that don't modulate current according to charge condition, will fry your battery over time.