If I give away a book on my website can my readers still review it at Amazon?

Yes, but they won’t be able to mark it as an Amazon Verified Purchase in their review. That’s reserved for actual purchases or if they got it for free during a free promotional day if you are using KDP Select’s Lending Library (in which case you can’t give it away on your website until un-enrolling the book.) The customer will have had to have spent at least $50 on any products on Amazon in order to leave reviews, but will not have had to purchase your book specifically.

Note that if the person borrows the book from Kindle Unlimited, then they will not be able to leave a verified purchase review, but can still leave an unlabeled review.