Do the American have any car safety regulations like the UK MOT test?

You can pretty much "roll your own" around here. There are some requirements, seat belts, bumpers, wind shield, and a few others. Some states have stiffer regulations and "smog" tests" too. Some states have "safety inspections" that are required and some have both. But only California (that I know of) has the socialist mindset to do as your government does. Freedom isn't free, we paid for ours.  more