point of order: the master cylinder is on the handlebar. Do you mean the piston in the caliper? At rotor level?
Everything mustbe clean and shiny to ensure function. Yes you should be able to push the piston (via the pad) into the caliper, if the bleeder is turned open or removed.
Not really a kit for the caliper. Disassemble, clean everything, replace the square section ORing (it does the lions work of retracting the piston).
rebuild kits available for the master cylinder.