http://www.teamviewer.com same as webex or gtm except its for FREE!
There's also the Windows Remote Console, and tools like VNC (Virtual Network Console) which perform similar functions but are standardized so the two machines don't have to be running the same operating system.
Yes. GoToMeeting.com and WebEx.com both provide that as part of their conferencing systems. I'm sure there are other companies which do so as well.