did you connect the remote turn on wire from the deck to the power antenna wire of the harness? Check your connections and make sure they're right... I cant think of any other reason why it wouldnt work with the alpine... unless you bought it used and the previous owner burnt out the turn on circuit.

About the second question, you definitely can power the antenna trigger from the ACC wire, you wont overload anything, the antenna only needs a small amount of power for a trigger.