No, police officers do not have the authority to exceed the speed limit without a valid reason.
There are police officers at every level of government. Federal, state, county, city and agencies all can have sworn police officers.
Is conveyed by officers receiving a commision.
Yes, Immigration and Customs Enforcement (ICE) Officers are fully sworn and accredited federal law enforcement officers. They are empowered to arrest for ANY violation of federal law (and local law IF deputized to do so by the appropriate authority).
The same authority that enables them to carry firearms.
... are known as liaison officers
Past officers no longer have the authority of presently serving police officers.
express, implied, and apparent authority
municipal agencies
No
Most agencies wear the badge on the left.
Warrant Officers get their authority from the Secretary of the Army, but remain specialists