In some states, an off duty police officer can write a speeding ticket. It will depend on the laws in your specific state. You can always go to court to fight the ticket.
It doesn't matter where they sit. If you are speeding, they can write you a ticket. How and where they are when they determine you are speeding doesn't matter. (Neither does the state!)
ticket deferral letter
When they write you a ticket, but you are not arrested. Examples of this are most traffic violations, i.e. a speeding ticket. More serious crimes will be an arrest, not a citation.
admit that you were speeding and ask for a reduction in speed to pay the ticket admit that you were speeding and ask for a reduction in speed so you can pay the ticket.
Yes, and some (especially highway patrols) do. However, most police officers will go out of their way to avoid citing another officer. This practice is called "professional courtesy," and it is somewhat controversial.
admit that you were speeding and ask for a reduction in speed to pay the ticket admit that you were speeding and ask for a reduction in speed so you can pay the ticket.
you bring the ticket into a motor vehicle branch and ask to dispute it.
No, city police in Illinois do not have jurisdiction to write speeding tickets on state highways outside of their city limits. State highways fall under the jurisdiction of the Illinois State Police or the relevant county sheriff's department.
My guess is probably not. It is the officers job to write you down for the speed you were clocked at. The purpose of the judge is to be an impartial official should you choose to oppose the ticket in court.
They normally will write you a warning ticket.
In some places they might, but here in my city, there is no official quota. However, each officer has to write somewhere near the monthly overall average for the entire department.
Yes. California peace officers retain their police powers throughout the state.