There are a few reasons your car’s defroster may not be working. One possibility is that the wire harness that connects your car’s defroster to the engine is not properly sealed. This can allow moisture and heat to escape, which can cause the defroster to not work. Another reason could be a clogged air filter. If this is the case, you will need to take your car in for service.
Yes, you can drive your car if the heater core is leaking. You will need to replace the entire heater core, so be sure to have a mechanic do this for you.