“Is there a way to do a batch render with different files?”
Do you mean rendering one project to a number of different formats or several different projects to the same format?
If it’s the former, the Batch Render script built into Vegas Pro can do this for you.
If it’s the latter, open multiple instances of Vegas or give Veggie Toolkit a try.
“is there a way that when it finishes rendering, Vegas can tell the machine to shut down?”
Here are two threads with a variety of options to choose from.
How to get machine to shut-down after Vegas finishes rendering?
Automatically shutting down PC after rendering…