"You may trade with a character that you land on by exchanging any 1 Object of yours for 1 Object of his."

Do I get to choose which object to take from the other character?

Yes.

Don't be mislead by how trading works in real life, just focus on "exchange any 1 Object of yours for 1 Object of his".

Same goes for the Merchant character from what I remember.

I don't think gold works any more, like I think it did in 2nd edition tho.