Grinding Noise & Vibration after ignition & while driving

I have a 2006 Mustang GT that has less than 5000 miles on it. After I start the car, I hear these grinding/vibration noises coming from around the manual shifter. It started by only happening during cooler weather starts, but now its nearly every time I start the car. The noise level would vary depending on weather temperature and how long its been since I previously drove the car. To make matters worse, it now will occassionally do the same thing while driving within the first three gears.

Also, sometimes when I change gears, I hear a rattling noise coming from the engine. Its very brief, sounds like something metal rattling, like coins in your pocket. It only happens during shifting.

Any ideas on the above two issues? Any help would be greatly appreciated!