Is there a way to tell if mechanical switched engine or transmission?

Dropped car off shady car repair shop. Been few days and they added a few more for what seems to be simple fixes.

I get maybe ordered parts. But my mind is racing that they are swapping part since low miles car.

Can I tell when I get the car back from like vin number? Would it match engine serial number or something? Just worried they keep stalling and shady. Regret even going there.

It's an 05 ford.

Dealership sold me a car with wrong sized rims/wheels and tires?

I bought a 2016 model car at Keith Hawthorne of Ford in January of 2018 and shortly after I had an issue to where when my car went over 50 MPH the whole car would shake, including the steering wheel. I had a warranty and called the place I got it from and they told me to take it to Keith Hawthorne of Hyundai since that's what kind of car I had. They informed me that my rim was bent and that my warranty did not cover that. I did not have any extra $$ to cover the cost and decided to just deal with it until then. Yesterday I brought my car back to Hyundai due to a recall and to get my car inspected and they would not pass my inspection because they told me I have the wrong sized rims and tires on my car which is causing holes in the plastic part above and around the tire. Basically my question is if there's anything I can do through the dealership I bought at for selling me a car with wrong parts and now causing me to fail inspection and have multiple issues?