the core and hose hold maybe a 1/2 gallon, if your coolant is old, you may want to flush it and add new coolant altogether. most of the time it will be ok.

and yes, try to keep the hoses full to avoid any air getting back in, some will spill out, just try to minimize it.

they also sell antifreeze testers, cost like 5 or 6 bucks, it will tell you how cold your coolant is good for.