I have a 2002 Mercury Cougar and it makes a loud grinding sound every time i brake. Sometimes it even rolls backwards when in drive. What could be the problem(s)?
These two issues are very unlikely to be related.
A grinding sound under braking, with no squeal when NOT braking, is typically rusty/gouged brake rotors. The fix would be to resurface or replace the brake rotors, and probably the pads while you are at it.
As to the car rolling backwards when in drive, I'd assume this only happens when the car is stopped and pointed up hill. If the hill is particularly steep, this may not be indicative of a problem with the car. If this is happening on slight hills, you should have your transmission looked at. You could start by checking the transmission fluid level, which is easy on some cars and difficult on others.