Answer to all three is yes. KeePass creates a file with your passwords, so you can do whatever you want with that file. I have it synced up to DropBox for easy access and protection.
As for is it safe, it's as safe as anything like that can be. The file itself is quite safe. The app is fairly safe in memory as well, encrypting important parts (do not store passwords in the comments field unless you enable in memory encryption of all data).
http://keepass.info/help/base/security.html
Of course if your computer is compromised with something that records keystrokes or something then they can get the password that way. Or if you choose a very simple master password it might be vulnerable to a dictionary attack by a very patient hacker.