Yes, on all of that. If the pressure drops off too much the system looses prime and that doesn't always recover quick enough when the fuel pump primes when the key is first turned, especially with a system like E53 where the regulator is in the fuel filter. You really shouldn't be looking at injector values at all at this point.
Maybe check the spark plugs while you are waiting for the fuel gauge.
This thread should really be called "hard starting cold" you could probably have a look at some of those type of threads as well.
