if you screen got broken inner, it will not waterproof. So you need go to a repair shop and fix your screen. since you are wondering after change a new screen will still waterproof, i think yes. for mostly screen repair, they will put a new iphone 7 plus waterproof sticker, so that your iphone will still "waterproof" . Maybe you can call a nearby repair shop and confirm with them.
no, ipad mini 1/2 is same digitizer but ipad mini 3 and mini 4 is different, ipad mini 3 you can change a digitizer by yourself easily, ipad mini 4 you can't, you normally need a lcd digitizer assembly for ipad mini 4, only if you are a refurbished factory have special cut glass tools then you can change ipad mini 4 digitizer.
that long home flex is ok to be replaced, if you have original home button with home flex which sensor working before, after you replaced screen and long home flex, the touch id should be work.
this normally happen during update your systerm, few years ago my htc had this situation before, is very hard for us to fix it our self, you need find some one to update your soft systerm etc, just check if it is still in warranty and give it to samsung repair center maybe better.