Yes
I am not sure they would do it because it's not safe to drive with a broken stud. If your stud is broken, tire rotation might be just a luxury at this point. I understand how things might be difficult - I drove with a missing stud for a month before I could fix it but it is not a safe thing to do and I knew it so I stayed off the highways.
Probably not, because its not safe to drive with a stud broke
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