What I do..
Go to the username box, alt-tab to KeePass. Find & highlight the KeePass entry, tap CTRL + V, it will then alt-tab back to your browser, it will type in the username, then it will tab and type in the password.
After this, it will wipe the clipboard.
Dropbox. Though I only ever update the database in Windows, so I can't comment on that side of things. Also I didn't bother with a keyfile, so I don't know how well that would work if you were to use one.
Personally I moved onto LastPass, though I appreciate some more paranoid types might not trust a cloud-based solution.
KeePass is perfectly capable, but I found LastPass was able to assist more on the Android side (though if you use LastPass on a mobile you need to stump up).