Well, make sure that you've done the 'Reset' as described, i.e. need to hold down both buttons for about 10+ secs until the Apple logo appears - this maneuver is often unsuccessful for some because the buttons are released prematurely - sorry, but not meant to be critical - I'm assuming that you have done the 'Reset' correctly.
Which iPad Mini model do you own (see below) - except for the original Mini, all can be upgraded to iOS 11, which may correct your issue(s) and likely download newer updates to the Kindle app. Finally, if you do not want to do an iOS upgrade, then the last suggestion for me would be to delete and reinstall the apps that are misbehaving; of course, may require getting all of your books back into the app. Dave