Lightning can strike many mile from where you leave and it can travel through the grid to you.
Virtually impossible. The co-ordinating gaps fitted on the first transformer the surge hits will divert it to earth. Ex National grid planning engineer. Any overhead lines which will be at 11Kv and certainly will not be many miles long. Outdoor substations will have surge diverters on overhead connections.
A broken neutral (mechanical failure) is the most likely cause of issues, The supply voltage can rise from 240V to 415V.
High voltage lines have a continous earth conductor at the top of the tower that bonds every tower which protects the lower conductors from a direct lightning strike. These days often with a fibre optic core for comms and line protection signalling.