Do cops commit violent crimes at 1/2 the normal rate because cops are less likely to be arrested or convicted?
Cops are less likely to be arrested and convicted for using force because they are trained on the specific laws governing the use of force. The travesty isn't that the cops get away with using force. The travesty is that the government provides this training only to police, and not to the general public. The public is woefully and dangerously misinformed as to when the law says they can use force. The only training most of us receive is from employers, and they don't teach the law: they teach a corporate policy designed not to protect people, but to shield themselves from liability.
For example, the corporate policy during an armed robbery is almost always "appease the robber". Give them everything they demand. Do nothing to protect yourself, the business, the money, etc. Robbers have taken this to mean that carrying a gun will ensure employee compliance. The lesson they learn is that the more they escalate, the less resistance they will face.
The law does not have this same "appeasement" strategy. The law considers an armed robbery to be a credible, criminal, imminent, threat of death or grievous bodily harm to every customer and employee present. Anyone receiving or observing such a threat is fully justified in using lethal force to stop the threat. The person who decided on a "career" in armed robbery after learning corporate policies doesn't even realize that they have placed themselves in grave danger from anyone who understands the law.
We should be learning the law governing use of force in school, so every last one of us realizes that armed robbery is suicidal behavior.
Am I twice as safe in the presence of a cop if I'm the cop's wife?
Easily.
I don't think you understand how high the rate of domestic violence is among the general populace. Cops are less likely to commit DV, but much more likely to be reported by their victims. The stereotype arises from this selection bias.
Am I safer near a concealed carry person vs. someone who just isn't carrying a gun?
Assuming you are not committing a violent crime, you are far safer next to the carrier than the random persons. It's not even close. The violent crime rate among the general population is an order of magnitude higher than among concealed carriers, and most of that violent crime is committed by individuals who are not carrying firearms.
However, If you are committing a violent crime, you are in extraordinary danger from that concealed carrier.
You need to remember that "general population" doesn't include just you and your neighbors. It includes all the people living in those boarded up, abandoned homes located in that nearby urban area that you don't dare stop in after dark. The "concealed carrier" cohort excludes all the criminals in those areas that make the place unsafe.