Diablo – a conquest this season (12)

You can change skills whenever you want, but there are currently two penalties:

There's a small cool-down in which you won't be able to use the new skill, which makes swapping skills frequently in combat disadvantageous...

...And swapping skills will cause you to lose the "Nephalem Valor" buff that characters over level 60 get from killing elite monsters, which increases your magic find, causes boss monsters to drop additional items, and, since paragon levels were added in patch 1.0.4, also gives bonus experience.

See also the question on Nephalem Valor

Unfortunately, this is a downside to having RealID friends. Unless it's different in D3 than it is in WoW and Starcraft, your RealID friends will always know if you're online. As you said, if you're marked as busy, people can't join a game with you. If you're away, I think it's just cosmetic to show that you're not there, so they don't think you're just ignoring them (or are you?). The best option I can see in your case is to just mark yourself as busy so it ignores group requests.

Here's Blizzard's information on the matter.