Is there any way to parent proof a phone from themselves? My fathers phone is an absolute mess every time I look at it. When I passed him the phone, there was one home screen, and the default thing on the bottom launcher bar like phone, messages, browser. 

Now, there are something like 8 home screen with numerous duplicates of apps, numerous folders with even more duplicates of apps, folders on the launcher bar, I don't even know where the phone dialler is hidden at this point. Of course, there are all the strange apps that now inhabit the phone as well that promise to "clean" the phone and speed it up and various other apps of that sort. He also manages to disable GPS, disable WiFi, and disable cellular data from time to time among other things. 

When asked about it... well... he alleges that he never touches anything. 

I'm sure others have been in this position before. Is there any app out there that can do the following:

1) lock all settings like GPS, WiFi, Cellular Data, etc.
2) lock all icons on the homescreen etc. so that new shortcuts/folders can't be created
3) lock new apps from being installed

All of the above can be temporarily unlocked with a password or something like that. It doesn't have to be one app to do everything, even 2 or 3 would be fine... ideally free, but this is absolutely something I'd pay for.
Ironically what you need is a parental control app. There are many on the play store but the only one I’ve ever used is Kid's Place. They are all designed to do exactly what you are asking… Lock everything from GPS settings to installing app. 

You might also try educating your father with regard to touch screens. He is most likely handling the phone when the screen is active, unaware that every touch is changing “something”.