Ongoing intermittent rev jumping and other issues.

Hi fellow car enthusiasts. I’m hoping that someone out there can help with a problem I’m currently having. 
 

My Ford Fiesta Zetec S 1.6 TDCI (57 plate) is having multiple problems.

These are as follows: 

When you reach around 1.8 - 2.3k revs the car jumps forward and sometimes revs uncontrollably after throttle response (As if there was a flat spot). 
This is followed by a rattling / knocking sound.

The instant boost of power is as if someone has strapped a second turbo to the engine and the car is overall a lot faster and more responsive instead of how it would usually be, lumpy and slowish.

9/10 times this issue will flag a 'Engine System Fault' message on the dash. The car goes into limp mode after that. 

A couple days after I suffered these problems, I was driving downhill until the throttle stopped responding. I pulled over to receive a ‘Steering assist failure’. After starting the car back up, I got three minutes down the road, pulled over to answer a phone call and the engine cut out. The car was towed home and would only crank, but not fire into life until I messed around with the fuses (Making sure nothing had blown), took all the plastic covers off including the intake and began stripping the bolts which held the clocks (so that I could investigate the wiring condition). I took a chance and tried starting the car up, and it ran decently but with a harsh smelling white smoke coming from the exhaust. 
 

Moreover, there were two onboard error codes, DTC 1 - C100 and DTC - E510. (Through the hidden test mode startup, holding the trip button and turning ignition. This was until I took it to a garage and was given a diagnosis that the fuel pump had gone. Once that was replaced (including labour, £566.66), the codes disappeared And so did the white smoke. But the jumping problem is still there. 
 

I believe the image below is the fuel flow before the pump was changed.
 

I took the car for a little test drive after I had the fuel pump work done, and it seems that the jumping didn’t occur on a cold start, but would after about 10 minutes of driving. 

 

Can anyone help me out?