You can ask anybody you want to do an exchange with you. that works fine, as long as you can find someone who wants to swap. You can handle it mostly through private messages.
The organized swaps here are usually organized by/for the paying supporters, but you can always set up your own any time you'd like to.
For homebrew contests, you could check out the beertown.org website. That's a good place to start, and I know there are lots more.
Broken Leg Brewery
Giving beer a leg to stand on since 2006