i have a 10 dollar free shipping 3800mah from ebay.
battery life is not the best for $10 but it can make it the whole day..(moderate use!)
i have never seen any cases for extended batter but the battery does come with bigger back cover to accommodate the extended battery.
the battery i bought did charged with regular zte stock charger, it also charged with any regular usb cable.
as for the screen protector i simply use regular old 1 1/2 inch wide clear tape!!
this is only coming from what i have experience!!
hope it helps you!