It's very valuable legal advice, just like "cops can't lie if you ask if they are cops".
Thats sarcasm.
Your car enjoys a limited expectation of privacy. Th OP IDs the most common exceptions to warranted search, however, if the policeman has PC for a search then he has it for any and all containers which could possibly contain the subject matter of the search. The locked box with consent is an issue I've never heard of before, but I wouldn't rely on it being protected.
The reasonable suspicion bit is for stops. It is a lower standard and allows them to use the information gained from the stop to try to obtain PC.
JMDB, your buddy probably heard "open carry" was illegal some places. There is no limitation to carrying your gun in your car on the seat, but like other posts mentioned, not advisable.