Yes your media will go offline as FCP will look to the path that it was originally given when you imported or digitized the media. However, once on the new HD you can Recconnect the media through the file menus or by right clicking on the shot in the timeline and hitting recconnect media. This also works if you are selecting all of your media in the timeline or browser for that matter.
As far a formatting your drive I would reccommend using a seperate drive, even if it is internal, for all your media so it stays seperate from your system OS and your other software. If you really can’t afford or acquire another HD then I would suggest simply making a folder that you will always digitize to or import to so that you do not have multiple places your footage will go to. Some people leave the default FCP folders but I prefer to make a Project Folder called “Project XXX Media” and then tell FCP to use this as the Scratch folder. Helps keep me more organized.
You should however have very little problem with keeping your project files on the system drive as they rarely take up massive amounts of space.
Good Luck
Bob