Anyway, really easy. Get a ship that can land with a hanger bay, and load up the vehicle. THen go to where the Corona is and from the landing ships vehicle cargo page, choose the load into option to move the vehicle over. No docking needed.
Party slot size refers to the number of squadron slots that entity occupies. You have 12 slots for your squadron. Therefore an entity that takes up 12 slots would not be able to be partied in a squadron with any other entity.
What you can dock inside an entity like a ship is determined by the cargo capacity (both volume and weight) of the host ship which limits the maximum that can go in. Then the ships etc you dock inside have their own weight/volume (not capacity) that is used to determine how much can fit.