"Up to 20" refers to how much you can withdraw in one go. I can tell you from painful experience that there's no limit to how much you can store in the Gift Box and that items only disappear once they reach their expiration date. (The gift box will count only up to 100 items and gets increasingly laggy the higher you stack up).

Obviously, FKG rewards from playing IWZ go to the FKG account and IWZ item rewards gained from playing FKG go to your IWZ account.