The LR specialist should be using JLR software call SDD, which has the facility to save each diagnostic session, and print out that particular session too.
Test Book was for the older LRs, and isn't relevant for the FL2 at all.
I can't see how a mistimed belt can cause a sensor to fail myself, as there's no actual need to touch this particular sensor whilst doing the timing belt.
There are no lock washers in the diff. The diff bearing which goes noisy is secured by a special nut, which has a pre-applied locking compound.
It's possible to make a mess of doing the pinion bearing, but there are definitely no lock washers.
Are you sure you're being told accurate information by this other garage?
Wow £4k for under £1k of work.
Sounds like you're using the wrong garages to me.
The first garage charged £2.500 and Land Rover charged £1.500 to put it all right? they have put on the notes planet gears as necc due to previously not used a lock washer so nut was not tight and swarf found in oil drained off diff. They basically said as it was not tight it broke apart as we drove! so the cam sensor fault would not be caused by the timing belt being out and the car driving badly/