1. Yes, the automaton can and will cure if HP is below the appropriate percentage. Automaton skill level to learn Cure is 12 (lvl 4 PUP).
2. You don't really have much of a choice with this one. Most of the items needed are crafting materials (which in themselves are crafted only) and cannot be purchased from a merchant. Prices will very from server to server.
3. Here are a few I use:
/ja "Light Maneuver" <me>
(Pretty basic one. Have one for each element.)
/pet "Deploy" <t>
/ja "Retrieve" <me>
/ja "Activate" <me>
/pet "Deactivate" <me>
/ja "Repair" <me>
/p {Automaton} TP: <pettp>
ADD Macro:
/ja "Activate" <me>
/wait 1
/pet "Deploy" <t>
/wait 5
/pet "Deactivate" <me>
(A little sketchy on the wait timers for this one)