As far as I am aware, you can buy the extended "Applecare" at any point in the
first year of purchase.
I bought mine for my Laptop 11 months into year one.
It is linked to the "device" not the person or country, so should be no problem
whatsoever.
If you have concerns, speak to Apple first.
yes you can.
I have bought Apple care in Chile, Usa, Canada and europe, with no problem.
You only have to register the contract in the correct apple website.
Anyway, applecare latin america, was not sold anymore in Chile.