does the wii have...

profiles for each person? like on the ps3 and 360...

or is it all one profile like the xbox, GC, and ps2?

well technically one since there is no sign-in option, but there are some games that use themiis as a "profile" to save data for each mii on your system.

So that the high score for one mii could be higher than someone elses, on the same system.

Yep, what the above user said.

They also have games with save profiles (I'm thinking Trauma Center and MP3 off of the top of my head).

Nothing like Xbox 360's profile system or however PS3 does it, if that's what you were wondering.

You can't see whether or not any of your friends are online or using the Wii at the time, nor can you see what games they have saved, etc. What you do got is a mailing system inwhich you can type messages to one another, send photos,and exchange Mii's.
If you want to play an online game like Pokemon Battle Revolution or Battalian Wars II with a friend, those games use separate friend codes that you need to re-add them in order to play them online, and that goes for each and every online game. They all use separate codes needed for adding.

Back with the profile thing, there are no profiles, unless you consider your friends' name and Mii face in your adress book one.