The DEF codes throw up as the DPF gets clogged by soot. Diesels go into a DPF regeneration cycle that burns off the soot, but you must allow the cycle to complete before shutting down. I know larger diesel trucks have manual DPF regeneration capability.
I was talking with one person last week whose F350 diesel went into limp mode. He had no idea it needed DEF fluid. I guess not everyone knows that stuff yet.
Negative.
DPF and DEF/SCR are two separate systems in the exhaust stream. DPF traps particulate matter, DEF is injected into the SCR catalyst to reduce NOx emissions. But you are correct that DPF or DEF/SCR can throw codes and put the car into limp mode.
I had a similar experience to your F350, but with a John Deere motor grader. Guys in the field wanted to refill it with water. I told them, LOL then you gotta have the tech come out and fix it because it has a quality sensor in the tank. But you do you. Good luck with that. They ended up going to NAPA and was back to work an hour later.