if im honest mate I would not know where to start.....would my car make any noises because currently the rear right hand side of my car is make loud creek/squeeking noises when on uneven road and I am not sure what it is(it sounds like it is coming from the front right hand side all the way to the back but predominantly the rear). the last two days it has got so much louder and getting a bit concerned. it sounds like something is loose or rubbing/hitting on something but I cant explain it
with regards to the admin fee you are right admin fee is down to the insurer but the insurers I deal with follow the principle I mentioned.
DVLA can take a while to register the new vehicle reg so if you change the plate on your car while DVLA are registering the registration to your car then I would recommend you tell the insurer when you change it because the car reg will not match what is on your insurance. it does not matter if DVLA have not registered the registration yet as long as they are in the process
when I did mine I went to the DVLA and got the docs signed and then they advised to change the reg ASAP. my registration was not registered for another month when checking all relevant databases.