Hello and welcome to the forum.
Your engine starting, running and then cuts out sounds like a fuel supply problem. It may be the filter is blocked up with crap from the fuel tank. Mine did that on it's first run despite flushing the tank.
Depending on the type of filter fitted, you will need to replace it or maybe dismantle it to clean with carb cleaner.
The bumpers are fixed with a bolt through the chassis tube. My front ones use the same bolt to fix the axillary light bracket.
Drivers side bumper by
marlinpeter, on Flickr
At the back the bolt is underneath the car.
Good luck fixing your engine running and finishing off the car!
...peter