Trade plates would not be needed, you don't need valid VED on a vehicle going to an MOT. It would be perfectly reasonable and legal to ask the garage to collect your vehicle, and drive it on their trade insurance.
In short, answers to your questions and a brief elaboration;
If your vehicle is on SORN, it does not need insurance.
If your vehicle is in posession of valid VED, it does need to be insured, even if not on the road.
For an MOT; the vehicle must be insured. Either yourself insuring it, or the garage using their trade policy, but does not need VED.
To enable the 'driving other vehicles third party' the subject vehicle, must have its own insurance.
Trade plates only count as a portable VED licence that is granted for use with connection to said persons business, they are not needed to enable a vehicle to be driven to an MOT station.
They do not have any insurance capabilities. However, a trade plate number would be added to a motor trade policy and to the MID in the same way a normal VRM is added.