Sorry for the delayed response, but that is a lot to deal with in one post...so here goes:
Question #1: If you are already being fired upon it is indeed legal to use the gun of the hog to defend yourself just as you would any handheld weapon. As soon as the threat is gone then you would of course have to then drive yourself. A word of personal advice about employing this strategy though. Over the years I have had several opportunities to try this when I knew it was allowed and I have come to the conclusion that most of the time it is actually better to stay on foot and there are many reasons why. The trurrets of the hogs respond and even move slower than the Mastercheif does. When you are in the hog you are litterally a bigger target than when you are on foot (try shoting a walker with a chaingun and then shooting him when he gets in a hog...you'll see what I mean). When in the hog you remove your ability to throw nades. Last but not least, think for moment how it could look to an admin...you should be willing to briefly explain a situation that can so easily look like camping...and that would just take that much mor time away from racing. In short, this is something that I rarely do because it just does not work.
Question#2: This situation is somewhat different. Again you are allowed to gun from the hog if you are being fired at but you stated, in this situation, that the hog was not firing. It is reasonalbe to assume an oncomming rocket hog is a threat, however if at some point it is obvious that they are not firing at you then you have to ask yourself "why am I still gunning frim a driverless hog?". The reason you would have started gunning was because the oncomming rocket was a threat, if it is no longer a threat you should not continue firing until they are out of sight..you should get back to racing as soon as the threat is gone.
Question#3: Just like the other situations....yes it is legal but I would not do it for all the same reasons stated above.
Question#4: You ended up with the right answer on this one...you can also briefly comment to the admins what you saw and we can watch that player for it in the future.
Question#5: When you see an "h" in hog chat (not usually team chat) it is simply a way the gunner has of letting the driver know who he has on his gun. The "h" does not stand for anything, it is just that the quickest way to get your name to appear in hog chat is to hit "h" twice and hit enter. That way your name shows up in hog chat...letting the driver know who his gunner is and letting you get back to gunning asap....that is all it is.
I hope this helps...feel free to ask anything whenever you get the chance, a lot of other guests benefit from these questions as well, so they are always welcome.