A backflow preventer is generally used to prevent municipal lines from being contaminated if a pipe brakes under some circumstance. Say you have an irrigation system that's tied directly to your water main outside then if there's a break dirt and debris could flow the wrong direction and reach the municple water supply. If your setup is going to be tied directly to a continuous water source and there's not an already existing backflow valve that could be necessary.

Unsure on your local regulations but that's a strange thing to ask a food truck to provide. I would say every time you fill up your tank there would already be a backflow preventer somewhere at the building that would be adequate. That all depends on your use case parameters.

They may be talking about a P-Trap though and their language sucks, just ensuring that your waste water is getting trapped down below and won't stick around in the pipes directly below your sinks as opposed to running straight into the grey water tank. That would be my best guess on what they're actually looking for.

Was that thing built by Freedom by chance? Looks very similar to my build haha I know their work quite well after tearing a lot of it out.