Non-Amazon are synced if you email them to your account, but I don’t think they are if you load them to the device manually. But emailing is no problem - there are browser extensions, Calibre can do it and, of course, any email app or service works. As I recall, copying a book over via USB results in it a ‘local’ version - but this may have changed, as I’ve just been using email for a while.
The weak spot for sync is the ‘cloud reader’ web app, which won’t show you personal documents, or notes from them. So if you make a lot of use of personal documents, you really need your device on hand (the iOS app shows everything, so your phone may do in a pinch - but I wish the web app was better).
The Kindle is still geared towards Amazon purchases for the best experience, which I suppose is to be expected, but it can certainly be used as a general reader, provided you know how to convert epubs. Most of the frustrations I have tend to be a result of shoddy formatting in the source file - the device itself is fine.
