You don't need to remove the engine cover - just the small section above the thermstat, held on by 2 small nuts. Look on the right hand side of the engine - just above the distributor. You'll see the flap. When the engine is cold it should be closed, but you can open it by hand (its quite stiff) If its open when cold the thermostat is broken. This isn't too bad as the engine will still cool, though it will take longer to warm up. It will need replacing before next winter.
If it is closed, take the car for a good drive, until the engine is hot - the flap should now be opening. If you think its broken then take out the thermostat and put it in a pan of water to boil. If it hasn't fully expanded by near boiling point, get new one.
Check your brakes before going anywhere. Sometimes reversing fast and slamming the brakes on releases them then resets the adjusters. But it sounds like they need checking properly, the fluid replacing and bleeding.