I own a business and have to have my phone nearby for emergencies, how do I maintain this but also cut off everything else.

Hello there! You have an option of "Do Not Disturb" in your phone. Make sure you set it in such a way that only your calls and alarms can disturb you from time to time automatically. Secondly, make sure to switch off your internet and there you go. You are now all set to be Fabulous once again! Cya!

I’m a software engineer, and I have to do occasional on-call shifts. On those days I keep my phone in my bedroom. I’m not sure if you can do it as well, but I cut all notifications, except the ones coming from our alerting system (one specific phone number and one specific application)

I think there best way is to reduce the apps on your phone. Most things can be done with a browser (use the bookmarks widget to quickly access common pages). If simplicity is your goal over commit to it. Give 110%. That extra 10% can come from a lot of places but one easy thing is to use only one home screen and keep you background simple too, like 3 colors max. Good luck friend.