1996 Ford Taurus

Alright im 17 years old, and I bought a '96 Taurus 3.0L 24 Valve DOHC, that is in very good condition. It has only 31000 miles but I am having a problem with my transmission. I am not sure how long the previous owner had this problem, but he did make mention of it. I have been driving the car for about 4000 miles and the problem does not seem to be getting any worse:

Shifting from 1st gear into 2nd gear there is a problem. It seems like, it takes it out of gear and then slams it into 2nd gear after about 2 second. Even if I am not accelerating hard your head gets tossed back a little bit. Under hard acceleration the RPM's sometimes hit red line. I can squeal my tires going into 2nd gear.I experience shifting issues in the other gears, but it is much less. Also trying to go in reverse is a trip, because the transmission slips and take a bit to catch, it takes me about 3000 rpm to get the car moving in reverse.

I know this has to be something with my transmission but I dont know exactly what.

I think it could be the fault of my speed sensor, because when I take my foot off the brake and begin to accelerate my parking/emergency brake light comes on. But then it turns off after a second.

Any help/advice would be greatly appreciated.
Any information.
i.E- if this is a common problem or not

Thanks,
Hages