Practice & regulations vary widely in AZ. Contacting City Parks may be your best option to avoid unnecessary hassle. http://www.mdhtalk.org/cf/city-regulation.cfm?st=AZ
I would guess no because of the digging.
Maybe... I've never seen anyone metal detecting there before however you probably can't dig up the ground at a public park. There are always City workers there so your best bet is to ask the city.
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