First, Blizzard will be adding private chat channel functionality in some form in a patch shortly after the retail release of the game. A long-requested feature, chat channels were not in the beta test and will not be finished in time for the shipping product, but will be added soon thereafter. This should help players organize with friends, clans, and communities prior to the planned group functionality, which was originally going to introduce chat.
Additionally, the second phase of the StarCraft II beta is set to kick-off in early July. Rumors had placed the second phase on July 1st, but Blizzard has not yet committed to a date. This upcoming phase should last a few weeks before eventually coming down prior to the game's retail release.
As for tournaments, Blizzard will be issuing a patch after release (via BigDownload.com) with "features to address the needs of location-based pro tournaments," though no specifics are given as to what these features will be. As StarCraft II requires a persistent connection to Battle.net and includes no LAN play, smart money is on this patch adding something functionally similar to LAN play for Blizzard-licensed tournament partners. Still, I would not expect LAN play to be added in for the general population.
Finally, Blizzard has announced that players in South Korea that already have active World of WarCraft subscriptions will be able to play StarCraft II using the same game time. The game will also be sold exclusively in a digital format in Korea for the time being.