[Puck Luck]

Not sure of other manufacture's rebuild kits, but Honda's rebuild kits are basically seal kits. Rubber parts. I'm assuming other manufacture's and aftermarket would be the same.

The piston is usually pushed out with compressed air. If its rust in there, air isn't going to push it out. Could maybe try large waterpump pliers. But if it does come out, like in that video, it will be rusted and pitted. (bore and piston). Wouldn't want to try to clean rust off the piston and re-using it. Not worth the risk on brakes.

If the bleed screw is rusted, penetrating oil might work or else try using a torch. But run the risk of boiling the fluid. If the screw still breaks off, then it has to be drilled. Not worth the effort.

If the pins are rusted, try pressing it out or torch. If there's pitting on the pin or bore, not as big a deal since its not sealing any fluid.

Basiclly, if its siezed, metal parts are rusted and can be a bitch to take apart and good chance you have to replace that rusted part within the caliper.
Its fine to rebuild it if its leaking fluid because of old seals or if the piston boot or pin boots are torn and all the metal parts are still in good shape.

If its a rear caliper with a e-brake mechanism built in, it gets more complicated and definatley not worth trying to rebuild