To get this to work, you’ll probably need to set multiple arguments to get exactly the way you want. In situations like this, I usually start by settings the public argument to false and then adding in everything that I do want displayed.
In this case, setting public to false also sets publicly_queryable to false as well as exclude_from_search to true, both of which it sounds like you want.
I don’t know that you can remove the permalink from displaying beneath the title, but you could easily enqueue a stylesheet on the admin that hides the field.