Boat trash,

To answer your first question about how to remove the heater core, you have to remove the entire dash and then you can get to the heater core. very often the cores are the aluminum ones with the crimped-on tanks and all one needs to do to seal the leak which is often along the seal is to take the unit to your local radiator shop and have the seal crimp recrimped. Then have the shop pressure test the core and if everything is ok, reinstall. At that point, you should be good for a lot more years use.

Obviously, the job will take the better part of a day.
Ben