1.- why auto-* upgrades are important? For instance:
This depends on what types of idle you play mostly. For the normal idle "Campaign" this comes down to whether you want to do less clicks to finish the level. So, ultimately it's your call. For battles (where you can only do one action every 4 sec) and challenges (where you cannot do any manual actions at all), automation is key! But still, you should check if the automation does you any good. Auto-Smelt is pretty much useless, if you don't have any automation that uses alloys and items (like Auto-Sell and - in case it exists - Auto-Tech Unlock).
If you don't have an automation maxed (like Auto-Conquer) it won't be able to waste all your resources (armies) on something, so if you want to do anything specific, either do this before the automation can get active, or just temporarily disable the automation.
2.- why statistics are important to activate?
Well, the first levels this is more about convenience, the later levels are more about stuff you wouldn't know otherwise, like revealing the whole tech tree. But, even the mine upgrade information gets interesting as soon as you have techs unlocked that boost mine production, or you unlocked some ore production advancement or use a mine boosting artifact. The factors are plenty and therefore, calculating the outcome of an upgrade by hand might not be that easy for higher levels. Still, the wiki has a bunch of resources that CAN make the early statistics useless if you are willing to spend the brain power yourself.
All in all, both the automations and the statistics are about convenience first and foremost. Decide yourself how much APs convenience is worth to you.
Edited 6/13/2021 01:31:23