Well my van has been written of twice once cat b and five weeks ago cat c ,never had to put it through a sperate mot or test and never had to return or apply for a new log book,bought hundreds of write offs over the years and the only test i know of is one to have a note put on the register to say it has been repaired to a good standard.there are a few garages that do this but in my opinion you would struggle to put even non write offs through as the test is very thorough.in answer to your last question yes it is harder to sell a written of car as most members of the public will run a mile a soon as they hpi the car ,it is also ileagle not to admit to the car having had damage if asked by the buyer ,but you do not have to declare this if not asked ,but to be honest i always do as it is not worth the grief when they come back to you when they do find out .