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Yes you can level it by repairing walls but its very slow way to level the skill line.They also work hand in hand so as long as you level up so as long as you earn AP you level up the skill line.
Both Support & Assault level at the same time regardless of how you are getting the AP. Repairing walls & doors is a good addition to getting AP but it shouldn't be your main way of getting AP. Defend keeps from attacks & stay inside the outer walls of the keep until the d-tick comes in.
You might want to try to heal your allies instead. It rewards much more AP than repairing walls.
Get some ranged and AOE healing, find allied groups and run with them. That way, you have a good chance to stay alive, get used to the combat mechanics and earn some AP.