Well.. that really depends on your state. Here in Vermont, we don't need permits so I can carry however I want. Alaska, Arizona, and Wyoming are also like this. In New York, even owning a handgun without a permit is a felony. In South Dakota, it's a class 1 misdemeanor. In Colorado, it's a class 2 misdemeanor. So on, and so forth.
Each state has their own laws; in most if not all it's illegal to carry without a permit. A lot of states have exceptions if you're in your house or place of business. Again it varies by state.
Now, about ID laws, that again depends on the state. Some states have stop and ID laws (which means if a police officer asks you for your ID you are required by law to give it to them). We have some firearm related Supreme Court rulings which protect us from harassment, most notably:
Terry V. Ohio - must be suspected of a crime before being detained\frisked.
Delaware V. Prouse - requires you to have a suspicion of crime before police can detain an individual.
Brown V. Texas – does not allow police to stop an individual and demand their I.D unless you suspect them of committing a crime.
Deberry V. US. - a firearm where legally carried cannot be the only cause for reasonable suspicion for a stop.