Well, the mutatordef is a rather abstract thing. It has nothing to do with it's GUI counterpart.
For what reason would you like to know if you have clicked on it?
As for your second question, it's easy.
Similar as with OverrideDefs, you can add a dict={} to ship plugins (in fact, you already do that).
Now, you can add a "modes": [ <Your mutator list> ] to that.
So if your mutator is in variable "mode", then you put mode there.
Now, of course you would prefer to have the mutator defined elsewere (in fact, you must, unless you want a lot of duplicate mutators

).
So, you have your file in autoload (say, MustangShipMutator.py)
Then you put in each ship file the following:
import Custom.Autoload.MustangShipMutator
But writing Custom.Autoload.MustangShipMutator.mode each time is a bit of a hassle.
So you put in this line instead of the import:
from Custom.Autoload.MustangShipMutator import mode
Now you can do {..... , "modes": [mode], ....}
This assumes that your autoload file is called MustangShipMutator.py, and the mutator within is called "mode" (as variable, not the real mutator name).