Unless your hiding something, they dont care what you own.
No they do not, but they don't have to prove that you bought the item in another country, you have to prove that you bought it in your own country.
I don't think that they bother much any more other than guns drugs and cases of booze, but they can still do this.
It's different with an RV as you would expect to have a fridge , stove and all kinds of equipment in there.
I filled out the Canadian equivalent to this many years ago and put on my big camera kit and binoculars, I havent updated it though.