I am looking to flip one feature (a cutout and holes) from one side of my part to the other, and then delete the initial feature. In sketching there is a "copy" feature that you can turn on and off to do this, but is there a similar way to do it for cuts, etc?
You can turn off live rules if you need to. And you can always try things and undo or quit without saving.
And yes, usually you can mirror and delete the original.