3 problems: no home button, locked and stuck in press home to upgrade

Hi Annelies,

It seems fairly evident that your first step here should be to replace the non-functional home button. You'll lose Touch ID, but at least you can get past the rest of the issue of it being stuck in the update process. You should be able to get a replacement for under $10 USD and that'll let you proceed with the update you're trying to accomplish. Here's the guide you'll need to do that replacement.

iPad mini 4 Wi-Fi Home Button Assembly Replacement - iFixit Repair Guide

P.S. DFU mode would allow you to do an update without the use of buttons or the screen via iTunes, but unfortunately you have to use the power and home buttons pressed together to get into DFU mode, so we're right back where we started with needing to replace the home button.

Don't throw away the old button; once you get your iPad back into an operational state there may be something we can do to help you get the original button working again so you don't lose your Touch ID, but let's address that after you get these issues straightened out.