You would have a coolant leak.
If the electric cooling fan(s) are not coming on that may be the problem.
They get old and become weak.
Bad Head Gasket. See a mechanic ASAP..
4 qts for the radiator alone. If the entire system is drained (block, heater, radiator) it would take 12 to 14 quarts.
Cracked head or bad head gasket.
If there are lines coming from the transmission to the radiator, it has a cooler in the radiator. If there are lines from the transmission to an external heat exchanger, that would be an auxiliary cooler.
the radiator itself no but the coolant that it carries has distinct odor Any paint on the new part could smell.
Heater core would be the likely culprit here.
You would have a leak, from either the pipes to the heater matrix (radiator), or the matrix itself.
The radiator itself probably holds a half gallon. The car as a whole would hold about 2 gallons.
If you are speaking about the two small hoses, yes. That would be transmission fluid.
It would be............... The Napoleonic Wars
The right side (passenger side) would be the transmission cooler lines. The plastic radiator tank is probably cracked near or at that fitting. Replacing the 12 year old radiator would be best.
an optical telescope
They're typically on the lower radiator hose itself. Make and model of the vehicle it's in would help.