Mercury Sable 1998 - starts with jerks

Recently I took my 1998 sable with 119000 miles for a 500 mile drive. On the way back, one day the car would shudder when stopped and the brakes applied. When accelerated, the car would move fine. By evening the problem went away.

the next day, the car drove for about 150 miles. Then when the car is driven at a 15-20 mile speed the car would start with jerks. When you release the brake, the car would not move forward. On acceleration, the car would jerk and start. Eventually after a few more miles, even after giving a raise, the car's rpm would increase but the car would not gain speed at the same pace. On checking the transmission oil, the oil was brown and diagnosed as "burnt".

what can be the potential causes for this issue? Urgent help is appreciated. Thanks.