I'm sorry but that is not useful. It is low resolution so you can't read the connection labels. Also this kind of diagram includes a proto board, which may or may not correspond exactly to the one you have. It even uses a different type of Arduino than yours.
So please take a pen/pencil and paper, and draw a proper schematic, take a photo and post it.
However, from what I know, some graphical LCD backlights do indeed run on 3.3v. The tutorial I followed also says to use 3.3v, and the backlight seems to run at a nice brightness level when powered with that, so I would not like to try 5 volts as that could ruin it.
And then for the part about the Mega 2560, I have replaced it with an an Uno and uploaded the sketch to it, but still no luck.