If you mean the plastic overflow tank, replace it. If you mean the plastic tanks on either side of the radiator core, replace the radiator.
blown head gasket or cracked head.
No, this could mean you have a cracked head gasket and engine pressure has entered the coolant.
A cracked radiator can not be fixed. A cracked radiator needs to be replaced . A mechanic can replace one in a few hours.
you are most likely leaking coolant and if your car should be overheating in a short period of time.
Both. The reservoir is the overflow. But in the event your radiator is low, your reservoir will back it up.
either a cracked head or a blown head gasket.
There are various things which could cause a cracked radiator. You should try to consult a professional on the matter.
A hot radiator releases excess coolant through the spring-loaded cap in to the reservoir, and when cooled the partial vacuum created by cooled radiator pulls it back in. A reservoir should be only about 1/4 full cold on a system that uses a radiator cap, some cars have a pressurized cap on reservoir and no cap on radiator
Why does the radiator fill up the reservoir
Yes
The radiator does not have a cap, instead, the coolant system reservoir is also pressurized and the pressure cap is on the reservoir.