If your brake caliper is sticking, then I don't think it matters if the pads are old or new.
It's just a sticking caliper and replacing it should fix the problem.
Squeaking could be a few things, were the rotors re-surfaced or replaced?
Did you install the spring clips on the new pads?
How old are the unit bearings?
An old/worn unit bearing could allow the rotors to not be parallel with the calipers.
That could cause squeaking and/or uneven wear.
Just some ideas...