You are 100% correct on the establishments serving alcohol.
You have the duty to inform only if you engage or are engaged by a police officer. A quick hello as you pass by is fine, anything more and you must inform the officer and allow him to secure your weapon if he feels it is necessary.
Gun buster signs DO have the weight of law in NC.
one area you may have missed is "any assembly where a fee is charged" basically if you have to pay a admission fee then no guns allowed. This includes movie theaters, mini golf, etc.