Agreed, and you raise some good questions. Rules should cover things like these. I'll offer some of my opinions on this.
Yes, definitely. This must be so simply due convenience. We cannot roll separately for every individual, it would be an utter waste of time. Also, convincing crowds certainly is something that is commonly done.
The results and the DC will depend on the situations (you covered essential aspects) and the argument being made. If the argument relies mainly on evoking the people's fear of fire, I think it should be an intimidation rather than persuasion check. As for how many are convinced, I think this is very good situation to use a degree of success. Higher the roll, more people are convinced.
Again, you can roll against the whole group, though here the main thing clearly is to convince the captain, who is in charge. I think if you come close to the DC, but not quite, some other guards might be convinced, but as they're not in charge it might not help you much unless you come up a way to do something clever with it. In order to try again, you need to come up with a substantially new argument; they already rejected your previous one. Also if the previous roll failed really badly, this might make their attitude towards you more negative, making further rolls harder.