As I have two armies with significant numbers of naval elements, I have had similar ponderings.
In relation to generals, I think the question is one of command difficulty (p.27). If a general is on a naval vessel, is he 'on the battlefield'? I would say that he is. Even though his element is not on the table, his troops know where he is and can see his vessel. (Indeed, I have to have something that clearly identifies my general's vessel so that I know which one he is on!) For sure, the men on his vessel will know that he is with them.
Following from that, answering 'yes' to both questions 1 and 2 seems reasonable, especially 2.
I am not entirely sure that I understand question 3. Whether a naval element is regular or irregular is determined by the vessel's type, not how it's crew moves on land. A naval and its embarked element do not a group make, so I suspect this is a non-issue. (As an aside, some crews might be particularly adept at sailing but then poor at soldiering to the point that they only become available at all when the naval has already been taken, typically marines.)
The example of marines, while not proof, reinforces why the answers to questions 4 and 5 are 'no'. I don't know of a list that allows marines to be taken without the naval they crew. In some lists, the only troops that can go on the naval are marines - they must go together.
Finally, consider the parallel of mounted infantry and their mounts: would anybody allow mounted infantry to move on their mounts and then dismount and move again and not call that marching? Or anything mounted - for example, Kn move and dismount as BdS, then the BdS move. Was the BdS element part of the Kn move?
Anthony