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EPUB3, yes. I don't think I have seen any EPUB2 having problem (except if it's missing encoding declaration)

How are you getting them onto your Kindle? Send to Kindle using EPUB does not work at all for me.

Amazon provides a tool that will convert epubs to kindle documents. (Poorly.)

They do this because the normal flow involved in publishing a kindle book is that you write an epub and submit it to Amazon.