You got a warning so no worries. Sometimes an officer will follow you and claim he was trying to catch up or safely pull you over...sometimes to see if you do anything else wrong or questionable in order to make a decision on possible tickets or just a warning. Either way, an officer is likely to claim it was the safety reason if questioned about it at some point..
Chefs, accountants, plumbers, landscapers, attorneys...all examples of service providers. You need a service provided and you can try to provide it for yourself or hire someone to provide it for you. In most situations, someone who spends all day every day providing such a service is likely to perform the service better than you can on your own. Not always better, and yes there will always be a cost, but a pro is a pro... That said, if you are tempted to represent yourself, better doing it...
Statute of limitations has to do with how much time elapses between the incident and when you are officially charged with something. With a traffic ticket, you are charged right there, same time and place. There's no statute of limitations issue. What you are asking is whether a state must simply forgive money due and drop the issue after a certain amount of time and the answer is no.
I don't know all the procedural aspects in AZ, but we have identity issues all the time. Speak with a local attorney about it and try to convince the court it wasn't you. Key to these matters is sometimes what identification in particular the officer was given at the time of the car stop(s).
I wouldn't expect the circumstances to matter much. The focus will be on how she actually measured your speed in the first place. You should probably speak with a local attorney about defense if you are worried about a potential conviction.
Officer "saw" something but you don't mention what if anything you were charged with. Hard to assess the need for an attorney just based on this information. It's likely you should consult with a local attorney if the charges were anything above and beyond a simple equipment (no lights) type of violation.