Heating and air conjust gives out hot air then smells of burning

Have you checked the blower fuse?

Are you loosing radiator fluid. sometimes the heater core will rupture and you will smell burn odor. also check for strange rubbing sounds or screeching coming from the blower fan motor. or engine exhaust manifolds are hot when car is on, make sure nothing is leaning on them which will cause a burn odor. Any odor coming from outside will find it's way inside through the fresh air vents.

have an accredited ac shop as an ac cannot produce hot air only cold air so that means that the ac is not working (leaks low on gas etc). The hot air is from the heater in the car and the smell is probably wire overheating or the resistors are burning.

If your heater is spraying a light mist through your vents it could be your heater coil. Mine did the same thing, smell rubber burning, then started a light mist through the vents. If you don't get that checked out, it could mess up your water pump and possibly your engine

you more than likely have a sciezed air con compressor. most modern cars have climate control which uses air con even when demisting and when engaged the electric clutch tries to engage but the pump itself will not turn, clutch will get red hot and burn your belts

the heater matrix is leaking from the sound of it ,they have plastic header tanks with a rubber seal and alloy centre .prone to failure when this age

Check your valve cover gaskets, bet they are leaking and that is burning off.

You will need to check where the liquid is coming from, It may be anything from Air Con, Fuel, Transmission Fluid etc..

The fact you smell burning plastic could be 3 things..

1, Brake pads could smell and burn down if they are on too tight (Had this problem with a trailer). Hence when you apply the brakes it could be squirting brake fluid out due to too much pressure.
- Check brake fluid

2, If the smell and liquid is inside the car (front pass side) it could be the air ducts. Under the dashboard you have air ducts etc for the fans and in car cooling (brother had issue with this)

3, Whatever the fluid is, it could possibly drip onto something hot, unusual for liquid to smell like plastic though, Auto transmission oil smells like fish.

Best bet would be the brakes. Next time you smell it just smell in the wheel mag and see if you can smell it, check the engine fluids often and dont use A/C (Air Con) as that does drip fluid (normal). If it is the brakes smelling you will need to have the lines bled out, tyre places may be able to do this, and possibly new brake pads

Good luck

Older cars leak. It is a sad fact. Small amounts of oil, transmission fluid and coolant hot the exhaust or engine block will give off a "burning" smell. It is good to be concerned, but likely it is not a major issue. Make sure all the nuts and bolts are are properly tight, and perhaps wipe down the reachable parts of the engine to help reduce the burn smell. As for the check engine light, most reputable auto parts stores can connect a small computer diagnostic tool to your car for free. It will give them any codes that have been set in your cars computer. Once those codes are written down ( have a pen and paper ready ) the can clear out the codes with their scanner and the "check engine light" should go away.

when a coolant is heated, it usually gives off a smell of a burning wire or a hot rod, but this will depend on what coolant you are using. It is either the coolant dripping to a hot part of the engine or the old replaced coolant still has some left on a hot part of the engine. some says evaporated coolants are dangerous, but that will, like what i said, depend on what coolant you are using. you may wan to consult the dealership that serviced your car and have it cleaned / checked.