I'm not sure why you would want to turn it off. Its like a clock, the numbers move occasionally but you do not notice it. Its not backlit or anything and not distracting. And as others have mentioned, it runs for months on the batteries.
no you're not doing anything wrong, these units can be quite hit or miss (ie if you buy 2 and keep them side by side, chances are they will display different readings). if you believe yours is defective you can do the rice bag test, or send it back and try to get a replacement.
Max is the maximum temp and humidity recorded. Min is the minimum recorded. If you push max and it says 49% then just push max again to get the current reading. It just saves the highest and lowest readings since you turned it on, they're not the current reading.