Can anyone please advise if I should leave the nick in the rear edge of the mouth, or remove it. If so, what is the best way to remove it, and if it is by filing through the mouth, what angle should it be to the sole of the plane?
The rear of the mouth, or the edge of the frog/bed, is relatively unimportant to the quality of the shavings. However, as it is chipped I would file it straight to prevent the chipping continuing.

More important is the mouth. It is quite worn in the centre. If you look at the photo you can see the shadow line change, indicating that the centre section is rounded over. This effectively increases the size of the mouth (as wood is unsupported in this area).

It depends on what you plan to use the plane for. A jack is a coarse plane and used with a cambered blade for thick shavings. The size of the mouth is irrelevant then. However, some like to use a #5 or #605 as a long smoother. In which case you would benefit from lapping the sole to flatten the area at the mouth.

Regards from Perth

Derek