Anywhere in the US
(in the US) Law Enforcement officers have always been armed.
It depends on the agency that employs the detective. In the US, almost all will, since they are law enforcement officers.
(in the US) Yes, all law enforcement officers are armed. In other nations; Some are armed and some are not (e.g.: the United Kingdom), in still others the police routinely carry even heavier weapons than what is the norm in the US.
In the US, they can. For example, security at nuclear power plants is privatised in the US, and private companies hire armed security officers to man these posts.
The lights that com out of guns are only used by police officers and the US army.
Some do, some don't.
No. About half the households in US have guns. Not every gun owner in the US carries a gun. The exact stats are uncertain, but simple logic would demonstrate that it would be less than 50% of Americans that carry guns.
Most law enforcement occupations require a firearms qualification, yes, although this can vary according to your location and specific function. In the US, parking enforcement officers are often unarmed, and motor carrier enforcement officers are in a number of states, as well. In the UK, Firearms Authorised Officers are normally the only ones who carry arms.
Yes. They would not be very effective against criminals with guns with just a badge.
Yes. It may require a license or permit, but yes.
There is a lot of disapproval towards gun ownership in the US.