without heavy usage, could last until the next day actually..true story, i've tried it..
regarding compatibility, yes they say got problem for certain apps..but so far i didn't encounter any problem to install or execute any apps..
each updates optimizes and fix the efficiency with the battery consumption..Asus tried their best to fix it, but best way so far is to invest on a powerbank.. 

after installing the apps, u can always check the setting>apps>moveable, to transfer large portion of the apps to SD card..except for the pre-installed apps which was already on the phone, every apps can be transferred to SD cards in ZF5..no need to root for that..
idk the benefits in rooting ZF5 other than can uninstall pre-installed apps and change fonts, can ask other sifus for that..if u mean optimizing the phone by tampering with the gpu render and etc, u can always enter the developer mode (tap 5 times in the About if i'm not mistaken)..

backlight as err lights behind the home buttons below the screen? sadly no

haha ask asus for that..how expensive backlights could be..if it's really crucial to u, u can always stick those glow-in-the-dark sticker below the homebuttons...