I'm not experiencing the issues you are describing but it could be because I'm on the .189 version which was just just released.
1. What do you want to customize? The ZenFone Game Genie doesn't have any game specific features like it does with our ROG Phone
2. What preferences? The only two settings someone would want to have activated every time are "No alerts" and "Lock brightness". "Lock brightness" will stay active even if you minimize but "No alerts" will turn off by purpose so you won't miss any calls when exit the game. I can understand that you think it should turn back off again once you return to the game and maybe we should change this but it's not a bug.
3. I called my phone 10 times during gaming and this issue never appeared. What games do you experience this in?
4. This must have changed in the latest version. I don't remember how it looked before but now you get a popup notification with the ability to put the caller on speaker right away.
I know there is room for improvement so I will ask if we can borrow functionality from ROG but there are no promises.