I have been an AD for nearly 10 years but was a local government guy before I retired. So to your questions:
Technically you are supposed to go with the forest closest to you but for me the closest forest did not want AD’s, the next closest only wanted AD’s to use on their forest so I ended up at a forest that while the forest land was the furthest away, they wanted AD’s and get me assignments nation wide.
The pay rate is the same for AD’s regardless of Agency and you can see it here. https://www.nifc.gov/sites/default/files/programs_documents/CPC/pay_plans/2022ADPayPlan.pdf
You are payed based on the job your were hired for. No H-Pay, OT, night differential, etc. just straight time.
I can’t speak to any kind of rotation. But if you have qualifications for the higher need positions you can be out a lot. I hold some Command Staff qual’s and have been gone as much as 120 days in one year.
You do have the option to turn down assignments but I would caution doing that too often, you will get a “frowny face” next to your name.
That should cover it. Contact your local agency and speak with who ever administers the program for them, often the Dispatch Center Supervisor. Good Luck