I have many projects in my Source Control folder, can I work from the server repository without mapping a local folder?
No, but you can configure you local workspace to only map to the folders you are interested in. You can also create more that one workspace.
For example:
$/TeamProject/Stuff/MoreStuff/ProjectA
to C:\Code\ProjectA
Repeat for other projects you are interested in.
You can now select a workspace to use in Source Control Explorer (and in Pending Changes). When you do a "Get Latest" on your workspace you will only get files you have mapped.