For being able to read your Kindle books, have a look at the Calibre sub-section. There are various guides on using Calibre to convert books.
Any of the readers not linked to a single supplier (like Google, Amazon etc) will support adding books via USB.
As for the rest, at least Mantano and Moon+ meet most of your requirements, though Mantano isn't free. I've used both on my phone and tablet.
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