Changing anti freeze

18 Qts is the entire system capacity. The only way to ghet all the coolant out is to flsuh the systemor dissasenbly. You still have cooloant in the heater core, (it is a good idea to turn on the heat when flushing and filling to get the coolant trapped in the core), the block still holds some and sometimes coolant will stay behaind the thermostat depending on motor. It is a good idea to change the thermostat and maybe even the radiator cap if you really want to hit everything.
Draining the radiator only gets some of the coolant, if you pull the thermostat and hoses, you will get more, but not all. That is why the Flush and Dill service is important.
Let me know if I can be of any more help.

The heater core is not that big and will hold around 2-3 Qts. There is still the cooling circuit in the engine and the hoses, it seems like a lot to still be in there, but it adds up.
The issue with the heat sounds like the heater core is bad or the heater core valve is disconnected or failed. The valve is generally on the firewall and will be on one of the 2 heater core hoses going in and out of the firewall. There is a cable that actuates the valve and when the temperature is turned up in the car the valve is opened allowing coolant into the heater core. If the valve has gotten stuck or sometimes the retaining clips that holds the cable in place can come lose and either situation keeps hot coolant from getting in the core and then the heater will not work. The other possibility is that the heater core is so corroded that is is either clogged or cannot transfer heat effectively enough to provide hot air.
If you find rust or corrosion in the coolant or it has had periods where it was not serviced for long periods of time, the heater core might need replacement.

Let me know how else I can help.