You can totally push it out from the bottom. You just need a skinny piece of metal to do it.
I’ve also been able to pull them out the top with a hook-shaped metal dentist’s pick, by stabbing into the plastic enough and then yanking the little plastic piece out. Pushing them out from the bottom is definitely easier though.
Don’t bother trying to repair the keycaps. I’m sure if you ask around you can find someone willing to sell/give you some spare Apple keycaps.
Also, to disassemble Alps switches, I recommend using something thinner than the screwdrivers in that Ripster picture posted above. (For instance, smaller screwdrivers.)