One thing to keep in mind with either option is that you will have to switch accounts on your Kindle eReader/app to access ebooks you bought on different Amazon websites. Switching accounts deletes all of your books, which you then have to re-download each time you switch. For example, I have ebooks I purchased on amazon.com (US) as well as amazon.co.jp (Japan). In order to access the books in the account I’m not using, I have to de-register the account I’m using (which deletes the books) and register with the other account (where I have to re-download anything I want to read). I never use my amazon.com account anymore as a result. One option would be to have separate devices for each account (for instance you could read from one store on your Kindle and the other on your iPad).
With that said, the iPad Kindle app does have dictionaries for multiple languages and you can install new dictionaries (as available) from the Kindle store. I have a screenshot of the menu for that in this post. I don’t know what the options are on the eReader.
I can’t speak to your question on Anki since I’ve never used it with the Kindle. You can export your highlights from the app or use them to create flash cards within the app. I’m not sure if the export will be sufficient for your needs. It does look like the Kindle eReader has a “vocabulary builder” feature that is not available in the app as far as I could tell.