No, not out of the box. they can set them or not. You may be able to do something with scripting, but then you'll need to maintain that when upgrading.
Not really, but you could use a workaraound. Remove the field from edit screen, add to each status (except closed) a transition which goes back to original status, add a screen which contains priority and set a condition that only some roles/groups can use this transition.
Now you have what you want.
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