When i turn off my heater or AC the fan keeps blowing until I turn off the car

Let's break this down.
1 Does the fuse blow when the heater is on, or just the AC?
Yes- Fan motor problem likely need new blower motor.
No- 2
2 Disconnect the AC compressor clutch wire. Remove the blown AC fuse, connect a multimeter across the sockets for the fuse, measure DC voltage across the two sockets with the AC switch, and Ignition switch ON. Is Battery voltage present?
Yes- The wiring harness has a short between the output of the AC switch and ground, likely a pinched harness.
No- The AC compressor clutch is shorted. Replace either the whole compressor or the clutch.

vent flap shutting off?

I would disconnect the fan connector and use contact cleaner to clean the connection. Usually corrosion. Also fan might be going bad (Common Problem).

its VERY likely that your heater core is getting stopped up.

The heater in your car works by circulating hot water from the engine into a copper or aluminum pipe coiled up in the dashboard. The heater/airconditioner's fan blows across it and the hot air comes out of the vents. This is why the heater doesn't work right away when you first start the car. It usually won't work until the hot/cold needle in the gauges is starting to rise up.

If your mechanic recently replaced the thermostat, its possible that there is air in the system which will result in less antifreeze in the car than it should be. If this is not the case, the heater core is probably stopping up and will require expensive replacement if it cannot be flushed clean.

Check to make sure the car is full of antifreeze IN THE RADIATOR, AND THE OVERFLOW JUG. Please be very sure there is NO AIR in the cooling system as well.

Scott

ac clutch is going out

verify the fuse first!! the blower is located behind glove box, see it under it and only need to remove 4 phillips screws!

If air is blowing but is not warm then most likely your core is clogged or needs replaced. try removing the two hoses coming from the firewall and run fresh water through each one until clear. This should help you. If no air is blowing at all, turn on AC and if no air is blowing then either then you have a bad fan motor or a blown fuse.

You didn't say which switch you were referring to. So, since you say the "heat" keeps blowing out, I asume that you do not mean the fan control only (which would simply indicate a faulty switch) but the "heater/AC temperature control". Check the vacuum lines (to heater and AC vent controls under hood first then under dash) for holes/cracks/breaks or if one may have come loose.

Yes, but more likely the fan speed switch is defective or the blower is defective

i would deff check the relay i had a problem with my relay going out on my 04 but i just ran my fan to a togle switch so i can turn it on and off when i want it on when im in dead stop situations like traffic and also when your ac is on the fan has to be on or your ac will cut on and off to keep your car from really over heating in a hurry if your not moving, but i also run my car at the track and it helps to keep it cooler when racing down the drag strip.