Yes 1litre 3 cylinder.
no years to far apart
It should. To better check, go to local parts store and check the Haines Manual...is should be for both Geo Metro and Geo Storm, just check that is bolts up the same.
compare the engine stamps on the block or head. You may need a book to see if they are compatible to swap out.
Your heater core may have gone out. Or you could have build-up in the lines.
Yes, just make sure the screws line up. Some model variations may not line up correctly.