I have Visual Studio Online (now VS Team Services) account as a part of my MSDN subscription. I managed to create a project there, set a workspace in my local Visual Studio 2013
The Visual Studio Monaco editing experience is currently available on a number of Azure Websites. A quick introduction and getting started can be found on Channel9:
http://channel9.msdn.com/Series/Visual-Studio-Online-Monaco
Especially the "First Steps" video walks you through the steps of setting this up:
http://channel9.msdn.com/Series/Visual-Studio-Online-Monaco/First-Steps
This is (not yet) available for non-azure website projects, but this is where things are heading without a doubt. I can't wait to get my hands on it.
No, visual studio online hosts your code repository in the cloud (similar to github) and provides you with a code browsing experience.
If you are referring to editing code in the cloud, see Visual studio online "Monaco", which only works on azure websites for now.
Here you go. Try this in MSDN Offical Site for basic programs
Microsoft Online IDE
One solution that I use is to create a small V/M either on Amazon AWS, Azure (or any other cloud service) and install Visual Studio on there, then RDC into the V/M. You can spin up the V/M whenever you need to or if it's on a high-availability instance, you can connect any time.
Using TFS online with this is great, as I can either work locally, in a disconnected state (traveling, etc.), check-in, then work on the cloud, and really never have to carry my laptop around.
It seems to be "POSSIBLE".
Could you check this article which I have just found, which would be something you want?
http://dotnet.dzone.com/articles/first-look-visual-studio
at its first section "Getting started".
I don't think you can currently, however it used Monaco editor, which is the same editor as sky drive uses for code files. So it may be that Microsoft are planning to add this in at some point.
Edit: Turns out they are planning on adding it, at lease for azure web sites, I found this article on tech cruch: http://techcrunch.com/2013/11/13/microsofts-visual-studio-2013-launches-with-new-online-tools-for-team-and-build-management-preview-of-browser-based-code-editor/