How VS2012 work with Team Foundation Service?

I am starting to explore the capabilities of TFS. Questions I have are as follows:

1. I'm am using TFS, are my source code (files) store locally on my computer and when I'm done, I'll push it to TFS or is it always store on TFS?
2. If all my source code and files are store on TFS and not locally, how do I test my web application? Do I just hit the play on VS2012 to run it locally on my machine?
3. If all my source code and files are store on TFS and there isn't a copy on my local machine, how do I get a copy of all my files and source code so I can take it with on my USB flash drive or do whatever I want with it?
4. The way I used to have is I've created a Solution within VS2012 and within this solution I have multiple folders with multiple projects/websites. Is this still possible with TFS? Or, do I have to create each project in TFS that responds to individual project or web application that I have?

Many thanks in advance.