I don't think that you're allowed to trade any DLC items, such as Hal's Rifle, Armor, or Sword. As for why your friend can't play with you on Knothole Island, it's probably because he only has the free version. In the free version, you cannot travel to Knothole Island. You can only travel to Knothole Island if you have the premium version.
When it says "Download the free version so that you can play co-op with someone who has the content", I think all that it means is that if a person without the content were to join your game outside of Knothole Island and venture into Bowerstone Market, they wouldn't be able to see the submarine and such. I suppose that this would cause the game to malfunction.
"Anything
![G o o d [Good]](/emoticons/g_o_o_d.gif)
in life is either illegal, immoral, or fattening." - Murphy's Law