From what I've heard you can as long as your not interfering with him performing his duties or trespassing. What is considered interference they can always detain you and make you wait for a judge to answer that.
Generally speaking, no. It is currently only illegal in Illinois. The ACLU is in the process of appealing a decision of the Illinois courts to the Seventh Circuit Court of appeals. They are expected...
If you are a police officer you would not need to ask. A police officer doing his duty will treat another police officer as any member of the public (if they are out of uniform and off duty).
The word "Police" generally refers to an agency empowered to enforce laws and maintain public and social order. The term "Officer" generally refers to an agent working for the agency.
If you are referring to "undercover" officers, plainclothes detectives, or "tactical old clothes" officers, they are not lying to anyone because they are not under oath to tell the truth.