You can take my game… when you pry my cold, dead fingers off the board!
From my reading around, it appears that the answers are (1) No; the Scouting role to resolve the Rumor takes the whole action -- as would make thematic sense; and (2) Yes; the Influence roll to resolve the Rumor would be one of the Port activities within a normal Port action -- as also makes thematic sense and seems to fit better with some of the card outcomes, though it is sort of asymmetric with (1). Anyway, I am grateful for whatever the expert opinion can tell me; thanks.
That's correct. Btw, it's on page 3 of the FAQ, in case you didn't know there was an FAQ. Have fun!
FAQ, Cutthroat Variant and Errata