I think you can do a fixed layout via KF8, which is the replacement format some Kindles can use rather than the older mobi format. As @susan_cassidy mentioned no Kindle eInk device can view an ePub. You must convert ePub to mobi or KF8 and only KF8 would have the fixed layout ability.
Unfortunately I cannot help you on fixed layout in KF8 as I've never attempted it.
EDIT: Oops I didn't see one of your questions. AFAIK, the K3 (Kindle Keyboard), K4S and K4B (kindle non-touch models both silver and the newer black), Kindle Touch, and Kindle Paperwhite can view KF8 and I assume KF8 with a fixed layout. All the Kindle Fire models should be able to read KF8 with a fixed layout. I'm not certain about which Kindle apps (Kindle for PC, Mac, iOS, Android, etc.).
Currently: Kindle Touch, iPhone 5, and iPad 3.
Last edited by jswinden; 09-27-2012 at 02:47 PM.