1993 Ford Probe ROUGH idle when stopped

I have a '93 probe and it has two main problems. 1). Whenever I come to a stop at a light or stop sign, the engine idles REALLY rough for about 3 seconds. It will then idle back down for a couple seconds and do the same thing again. Happens 100% of the time. Feels like my car is rattling to pieces.

2). I put a brand spankin' new battery in and it quickly loses charge. The battery was totally dead after 3 days of no use. What the heck is draining the the juice so quickly?

NOTE: about 3 or 4 years ago my grandfather had the whole car looked over and rebuilt/tuned/fixed. New motor mounts, timing belt, alternator, the works. Thank you for taking the time to examine my questions, I appreciate it.