Restoring an iOS backup to a device running an older version My iPhone has iOS 10 on it. My iPad Mini has iOS 9 which is the most recent version available for that device.

Can I restore my iPad Mini with a backup that I made from my iPhone? I only need my contacts and messages.
No. You cannot restore newer iPhone backup to Older iPad. If you want to restore that, you have to upgrade iPad to iOS 10 first. But since iPad mini only supports iOS 9, there isn't a way of doing that. 

But you can export contacts to your windows/Mac and then sync data to your iPad. Or simply you can use iCloud to do that. Since you haven't said you need another way of transferring contacts and messages to your iPad, I ain't gonna explain.