Unless you specifically created puzzles or programming to cause your objects to move when dragged what you are experiencing is the standard orbit camera rotating making it look like your objects are moving when you drag but it stead its your camera doing the moving.
Once you parent an object to the camera it will be locked in the field of view and it will no longer move with camera orbit. Common uses of this are menu items, logos, etc….things you want locked to the camera regardless of how it moves.
You can parent as many objects to the camera as you need.
On the other hand if you have created code or puzzles for drag move or rotate on all your objects you will have to disable or delete the puzzles/code attached to the objects you do not want to move or rotate.