No cars brake lights will work when the car is off, it's a simple fact of the way that cars are wired. Why would they wire something that isn't needed when the car is not running, to work while the car is off, all that would do is leave a failure point, I.E. what if somehow the brake light got stuck on, instead of turning off with the car, it stays on and the battery goes dead while you are in work.
The brake and clutch fluid systems are supplied by the brake fluid reservoir ( according to the 2001 Mercury Cougar Owner Guide )
You can view the 2001 Mercury Cougar owners manual online at : www . motorcraft service . com ( no spaces ) Click on Owner Guides
If the brake lights stay on that probably means the switch on the brake pedal that activates them is defective.
The brake system was not that secure
DOT ( 3 ) brake fluid in North America , DOT ( 4 ) in Europe
No.
Those are called the "Side Marker Lights".
This is usually cause by a stuck brake light switch on the brake pedal. Replace it.
yes
On a 2001 Mercury Cougar : The radiator is located in the engine compartment , at the front of the vehicle
For the 1999 cougar they have 2 different size brake rotors it sounds like you need the 276mm size
According to the 2001 Mercury Cougar Owner Guide : ( the fuel tank holds 15.4 US. gallons )