I currently have apps on both the google play market and Amazon market and have not come across any of the issues you have mentioned above. I am using ecplise and created the apk file using a certificate and used the same apk file for both Android markets.
As they are seperate markets and as you mentioend Amazon has its own authentication meaning google play updates are not an issue and therefore need to be done on both Markets.
Google Play vs Amazon Appstore
Finally, things to look out for is if you have any links referencing the play market you need to change these to the Amazon market, as Amazon will fail it otherwise (upload to Amazon market can take several days), hope this helps.