Starcraft – Running Starcraft 2 from different computers

According to a post by a Blizzard employee, you might be able to play with your friends no matter where they are:

Getting people online, playing and interacting is obviously the overall goal for the Battle.net platform, and that includes allowing people to play across regional boundaries as they have in the past.

Unfortunately, there are a multitude of challenges we have to overcome due to the unique regional account and billing options that didn't exist in the past. But those hurdles aren't insurmountable, and we are looking into solutions that will allow interested players to obtain access to other regional versions without having to buy another full copy of the game. Those solutions are something we're currently planning to have available through Battle.net Account Management within the first few months of StarCraft II's release.

Before that solution is implemented though, you're correct in that you'd need to purchase a US copy of the game on launch day to play in the US region.

However notice that he is talking about a potential future feature which may end up not getting implemented (or not implemented in a satisfying way), so in the meanwhile I would be careful about which version to buy.

There is one mission like that in the final few missions that give you an option between 2 missions and depending on what you choose it makes the next mission change a bit, but it is still the same mission.

There is also one hidden objective in one of the missions that will give you access to a secret mission that can only be played by completing this objective, this mission however is not crucial to the story.