1) yes
2) No. A true (and complete) statement would be "An aircraft can follow the rhumb line track A to B, in which case its true track would be a constant 090 deg, but the path will be curved. It can also take the shortest straight line route, a great circle, in which case the intitial true track will be less than 090, its final true track greater. The aircraft could also take any number of curved tracks other than the rhumb line between A and B."
3) See above. This is correct assuming you try to follow a rhumb line path, but why would you?
4) Will think about this. It is probably true, but your true heading will represent neither the rhumb line nor great circle track. The aircraft will follow a curved path to the north of the great circle.