It goes on a record. However, the record is generally going to be attached to the vehicle (which was parked improperly), not you (there's almost certainly no proof that you were the one who parked it).
Parking tickets don't generally matter unless you don't pay them. If there are unpaid parking violations when you go to renew the vehicle registration, you may have to clear them before you're allowed to do so. If a vehicle accumulates enough unpaid parking violations, it may be towed or the owner may be arrested or summoned to appear in court. Also, it's pretty common for the fine to jump dramatically if it's not paid before the due date.
However, these generally don't count as "points" on your license or towards raising your insurance rates, if that's what you were asking.
Arizona, and for that matter, no state, has a statute of limitations on a ticket. The ticket serves as notice of the violation. Once issued, the state can determine whether they declare an amnesty for unpaid tickets.
If you get a speeding ticket in Arizona, Missouri will find out simply because each state shares records with each other. So if you get a ticket in one state and it appears on your record, it will appear on your record in all states. Under the Full Faith and Credit clause in the US Constitution, each state must respect the judicial proceedings of each other state. So if Arizona tickets you for speeding, Missouri must respect that.
No
Yes, just like a parking ticket.
Statute of limitations will not apply to a parking ticket. The ticket itself serves as proper notice of the violation by the state.
Pay It
A ticket, with a fine.
There isn't one. Like a diamond, a parking ticket is forever.
there is parallel parking, emergency parking, parking on a hill, and prohibited parking. (at least that's what the handbook in Arizona says, but check with your state handbook.)
Not in any state that I'm familiar with.
a ticket is a record to your license reguardless of the state
Just having a traffic ticket is not a reason to forbid a person from leaving Arizona or any other state. If having the traffic ticket is part of some other activity that is under police investigation than leaving the state may be a problem.