Do I need an adult with me when I go and get my permit switched to a different state? If so, can it be any adult?

It has to be a parent/guardian, not any adult. You could be a runaway looking to get an ID in a new place.

You need whatever you would need to obtain a permit in the new state, if you were starting from square one, because you are. Whether that means you need a parent or not depends on the individual state.

Anyone claiming the rules are the same in all states is DEAD WRONG.

you need an adult. no, not just any adult. Needs to be your parent or legal guardian