I have a few questions regarding the aforementioned in the title. I have heard many discussions on these topics.

I know in the state of Washington, a police officer, regardless of where they are employed, all share the same commission card, and all have equal authority. For those that know, I am actually in the process of law enforcement testing, but a few questions come to mind, simple out of curiosity.

1) Are Federal Law Enforcement Officers/Agents capable of enforcing non-federal offenses, on a local level? For example: Can an FBI agent act as an officer of the law if they are witnessing a convenience store robbery?

2) If a State Trooper in the State of Washington is in pursuit of a felony suspect, and the suspect crosses the state line into Oregon, can the Washington State Trooper pursue, and continue to act as law enforcement in Oregon? Now, does this vary from state to state, depending on which states have agreements and laws that allow officers from other states to have equal authority in their state?

3) Can Military Police (Not DoD Police) act as commissioned Law Enforcement outside of their jurisdiction (their base). For example, can a commissioned Military Police Officer enforce municipal, state and U.S. laws on civilian territory?

4) Can a police officer (municipal, state or federal) enter a military base? If so, under what circumstances? Which of the following is true (or closest to true)
* Any commissioned police officer can freely enter a military base regardless of if they are on duty.
*Any commissioned police officer can enter a military base if they are in pursuit of a suspect who has entered the base, or whom they believe is present on base.
*Any commissioned police officer can enter the base with the permission from the base commanding officer, or guard on duty (or other figure of authority)
*Any commissioned police officer with a search or arrest warrant from a Federal Court.

5) There are U.S. owned properties that are "off limits" for citizens to carry firearms. Can a police officer, whom is not necessarily investigating a crime, but entering a post office for the business of mailing off a package, lawfully enter the premises while armed? I have personally seen police officers do this, but I don't know if it's qualified as "official duties", or if that even matters.

6) Are Specialized Federal Police Units capable of acting as enforcers to laws other than what they are assigned to? For example, the U.S. Secret Service, U.S. Capitol Police, U.S. Supreme Court Police, U.S. Pentagon Police., etc.

I know this is a lot of reading, and I have done some research on the topics, but can't seem to find definite answers. Any information with sources would be greatly appreciated.