99 conv gt leaks

Hey everyone, well I just got my first mustang and i love it. Its a 99 GT Conv 5 speed. I am having two issues, nothing big but none the less. Ok first after it rains alot or driving through a car wash, i noticed that behind the rears seat, where the top stow, its full of water! Now i did notice that on both c pillars the cloth had a strip of water from top to bottm and was damp. I assumed this is where it leaks but in the same placew on both sides. Could it be the outside seams?? can i seal them??

and second is this, after a accelerating pretty hard from a stop to say 90, then coming to a stop light, to a complete stop the engine sometimes just dies. Now I had a vacuum hose replaced because it was constantly dying, and after it was fine except for this. It starts right up and is ok after it dies, but it does it occasionally. Its annoying but tolerable. Could it be something else, or is this normal??

Any help would be so greatly appreciated!!!!:worship