1) The best you have is Smart Call Handling - only Calls. If you want the Samsung stuff for other Sounds/Notification and Device Sensor interaction, you'll need a 3rd party app.
2) You can get "Tasker" or another Automation App - and it will be able to do this, and do (1).
I'm tempted to try another app other than tasker at the moment - as I feel like something fresh... For new users, Tasker can be a bit daunting, because unless you find a good tutorial, the UI isn't as friendly as the other Apps available now.
... Smart Lock is built in, and works in the opposite way, it detects when you have the phone with you, and can keep it unlocked.
When you have apps that start changing Screen On and Screen Off, I recommend checking Accessibility Settings, and make sure that "Power Button Ends Call" is Off. This way, you will always be able to turn the screen back on, incase an app fails, or sensors fail, and you are on a call, and the screen goes black.
3) If you're on Nougat, Swipe down, and swipe down again. Brightness Level Bar should appear.
Probably not just Nougat, and everything from Lollipop and Up.
Samsung Smart Stay == Sony Smart backlight Control
Welcome to Sony, where your phone will be less filled with proprietary apps, like Samsung.
My last Samsung was a XCover 2, on 4.1.2 where 400MB of my 1GB storage was used before I even started using the phone. So I don't quite know what else is available on the new gen... aside from some of the Voice stuff, and side bar.
