Ford fiesta trembles and pulls when I start to accelerate

indicates failed wheel bearing , no disc pads or damaged disc rotor
Take it to an accredited professional brake shop for a proper diagnosis

Ford Fiesta Start-Up Flaw (CPU-Based) - YouTube

? 1:54
www.youtube.com/watch?v=Y78GTNBytSQ
May 29, 2012 - Uploaded by georgef551 I found a start-up flaw in the Ford Fiesta, when I occasionally tried to start the car quickly, and... ... this happened. I had them either fail to fully turn over, or other CPU-based starters wouldstart up the vehicle. ..... Ford Fiesta 2004 Lx 1.4 petrol mk6 won't start help ! ... 2012 Ford Fiesta Zetec 1.6 TI-VCT. Start .

Gas? Diesel? Size of engine?

On most cars today if you step on the pedal you change the t.p.s..throttle position switch.and cause the computer to get a wrong reading.

might just need a good tune

Have u checked spark plugs.?

Sounds like timing is off

check your fuel pump? you mass airflow sensor could be damaged or need to be cleaned

First-NEVER add anything to an automatic trans.
Your vehicle should use Mercon V --PERIOD
Change it at least three times, to get the Lucas out.

Have the TPS Sensor checked out.
You most likely have a Tran Pack Solenoid going bad.
It is bolted to the valve body. You can do it yourself

wiggling or trembling are mostly cause by the front wheels.
it could only be unbalanced air pressure of the tires.
if not, it could be loose tie rod ends connecting to the steering wheel. fittings might have been worn out already and needs to be replaced.
to check whether if which side is causing it, lift or jack the left or right tire, then manually try to wiggle it, push or pull it, try every possible way to determine and looseness on the wheel. do the same on the other front wheel.
if one of then is loose or wiggles as you check, then there is a loose part on that wheel. check carefully.