1st paragraph) Park up with the engine off and not in traffic is legal. You could argue that 'being on the road' is in traffic by definition, even if the engine's off and you're parked on a road side out of 'traffic', in the same way as the famous line of 'if he's not interfering with play, what's he doing on the pitch'. But I don't make the law.
2nd paragraph) It isn't about me, it's about people using their phone illegally. I don't do that, so any other non illegal issue (heater etc) isn't about me. However, I don't mind backing you up with a signature if you wish to try and make it like phones- illegal. There is still 'driving' when being distracted in the law. I'd imagine is someone hit someone and caused death or life changing injury, the police would be all over it with the car's ECU or likewise if suspicion of cause, even if the distraction wasn't looking to see the hamster doing 11 spins a minute on a tick tok upload. Sat navs use to is against the law, going by that link earlier.
3rd paragraph) Whatever the law is.
4th paragraph) 'Law does make a special case for phone use in cars but the underlying point is all about due care and attention. Can a driver stood some time at traffic lights quickly (as in as quick as changing a radio station) glance at their phone to check the status screen safely? I would argue yes,
Again, if you wish you could argue for a law change to allow 'quick glances' at mobile phones when in stationary traffic (or similar). Currently it's against the law to do so. So hopefully those who do it will get their points and hopefully get off the road and/or see their insurance rocket.