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Yes, Arizona will extradite a wanted suspect charged with a F1 (1st Degree Felony) back to Ohio.
Yes
No.
County's don't extradite from other states, states extradite from other states. It can depend on how badly they want you back and whether or not your name appears on the interstate NCIC system as wanted.
Yes
The decision to extradite is normally made on a case by case basis. If it's felony bad check it will likely he handled differently from a felony assault.
Yes, however, it is unlikely unless the charge is a felony. For example, Nebraska most likely will not extradite someone who is wanted for skipping court on a misdemeanor.
Springfield is the capital of Illinois. Phoenix is the capital of Arizona.
Yes.
If there is a warrant issued for your arrest regarding the missed appearance, yes.
Will new mexico extradite from arizona for a mistermeanor DWI
All US states and territories honor each other's requests for extradition. Most states WILL extradite for felony offenses.