I see a Database.db file with size zero bytes on my Macintosh HD
Is this a system file? i am not sure if this is something i can remove or the purpose of this file
You're probably fine, but it depends and since it's taking up no space, no good reason to delete it yet. It's simply a database file put there by something (again, probably not OS X.) You should attempt to narrow down what application is using the file (see this post) and then either keep it or delete it as appropriate.