I think it is allowed. I have seen inflated jumping castle installed for a birthday party when I visited last time.
Check Parks&Rec website. Jumpers must have city approved insurance. There's a list of specific vendors that are signed up with the city for rentals.
Yes, a jumper is usually loud. Its because it uses a generator, plus you got kids screaming, having the time of their lives...
Not sure, call and check
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