Vegeta seems to take it as Goku's full power pretty immediately. He curses Goku for always being one step ahead of him. I think the overall point here is that Goku's power is so outrageous, it has to be his full power. Right?
As time goes on, doubt creeps in their mind. I don't think Piccolo heard the conversation, he wouldn't have to ask. He seems to have figured it out throughout the year while training in the Rosat. Piccolo was probably gunning for Goku's ridiculously far away power gets somewhere around it and starts figuring, hmmm, perhaps Goku has more in the tank, if I know Goku... Shit he probably has way more.
I think that's Piccolo mentality when he speaks to Goku. He is kind of showing off that he knows what's up, even though he hopes he's wrong. He ends up feeling foolish for hoping he was useful.
Trunks gets straight up herbed up in the corner. Like oh shit, I'm doomed. We never see any confidence at all from Trunks, he knows he's fucked.