When the scene shifts to the British Men of letters and there's a close up of the registration plate on the car it is a type that doesn't exist.
Firstly, it has a flag at the left hand side. This is a European-style plate which is not used in the UK. Although it is not illegal it would be very unusual to see.
Even if it were in widespread use it would have a Union flag and not a St. George's Cross as England is not recognised as an independent country but is a component of the United Kingdom.
Towards the end of the episode, when Sam goes to get "Chuck" some water: When Sam lifts the glass, you can see that there is already water in the glass towards the bottom left of the screen. And while there is a water pouring sound effect, you can also see that Sam isn't pouring anything.
In Hell's Angel (2016), Rowena healed Amara after the angel smiting. Since the plan to kill Amara required time, Rowena could have tried to heal Chuck/God to gain them some time, even if she could not completely heal him.