The marquee outside the theatre:
The show is to see a monster. Its a monster show. So yes, the idea was that rich people got to go in and look at a monster for a few minutes. Sounds boring to you and me, maybe, but in 1933 thats a big day out on the town!
Denham could not have kept it a secret, in spite of what he may have said. Kong arrived on a giant boat and was unloaded for all the world to see. Rumors would have flown.
Denham would have kept him chained up like that. Exactly as he was. Denham was a jerk, he never intended to keep the ape happy or well taken care of, just wanted money.
The police probably knew who Kong was because the whole town would have been talking about it. Giant ape arrives on boat, Broadway show with Kong in big bold letters on the marquee. Yah, they knew.
Here is my question about the movie - Kong accepted sacrifices by the natives of Skull Island and in return he left them alone. That was their bargain. So, in light of that, was Kong a sympathetic character who should have been left on his own, ruling over the natives by threat of death, or is he a raging monster who had to eventually be destroyed?