2003 Ford Expedition Could this be a fuel pump problem?

We just noticed about 1 month ago, when we get to around 40 miles per hour, or after stopping at a red light, our truck starts making a noise as if almost it is going from a V4 to a V8. It usually happens when we hit 40-50 MPH, and going up hills.
It seems like the car is "tugging" along and we accelerate to cause the noise to stop.
Also when we are in idle, the car makes a noise as if it wants to shut off. We actually thought someone had bumped into our bumper, because the car shook a little, but today it has been making the noise often, to the point I believed the car was going to just die right there.
So basically the car gives a pulling sensation when going up hill or at 40MPH.

Transmission has never been replaced, we change oil regularly. About 9 months ago, the heater stopped working in the rear of our car, and a knocking noise comes on when using the air conditioner in the back. What do you recommend the problem is and how much would this be to replace? We are in Florida, and our car ran out of warranty at 85K.
Help please!

We are trying to figure out an estimate before hand, because due to no warranty we must pay $100 for a diagnostic alone!