Does Google Drive sync with Local Folders? e.g. I have a folder called work (c:/work). I drag that folder to Google Drive Desktop, it syncs. Thereafter I create a new file in (c:/work). Will Google Drive sync that new file, or must I drag it into Google Drive Folder manually.
Not in that way. The desktop portion of Google Drive works essentially the same way as Dropbox: There is a special folder (usually called "Google Drive") in your file system. Whatever you add to that is synced with Google Drive. Whatever you remove from there is removed from Google Drive and no longer synced.
If somehow I lose all my files on Google Drive Web. When I login to the Desktop Application, will it sync and remove all my files, or will it sync the files in the Desktop App back into the web account.
How would you "lose all your files"?
If you remove the files yourself via the web interface, then, yes, they'll be removed from your desktop file system (assuming your PC is running and the app can connect to the Internet). However, they should be in your "Trash" folder so you can recover them.
How else would you lose them via the web? If you lose access to your account then the desktop sync app won't be able to log in and sync your files, so they shouldn't be touched.
There's not really a "login" to the desktop app after you've set it up. It runs in the background and you don't really interact with it directly. (Again, very similar to how Dropbox works.)
Are there any other limitations as well as more efficient methods of using Google Drive for my work?
That's rather subjective and not really answerable. We don't know how you work.
You should have a look at Google Drive in the Help Center.
In order to move the file, you'll need to add it to "My Drive". Until you do that it's only shared with you and you don't have rights to do much of anything with it.
Click the "Add to My Drive" icon/link. Then you should be able to do what you want.
Best Answer
I'm afraid without a local client those are your two options for moving files.