No
No.
No
yes
go to www.servicearizona.com
No you cannot. You will have to get your Arizona license reinstated first.
With a suspended license in IN will I be able to drive a 49 cc scooter in AZ?
None
There is no prohibition against registering your ownership of it - you just can't drive it.
Most states check on previous licenses when a new license is applied for. If a license is suspended in another state, it is unlikely a new license will be issued in another.
Your AZ license will be suspended if you don't pay your speeding ticket (or any other ticket). See first related link for a statement of the consequences, second related link for how to get your license reinstated after suspension. I found both of these at the third related link.
Yes, a suspended license can show up on a background check, particularly if the check includes driving records or motor vehicle history. It is important to be honest about any license suspensions when asked about your driving history.