The 16Mhz crystal on the Gamebuino board gives the clock to the main MCU, the ATMEGA328P, so it runs at 16 millions instructions / second.
These kind of
screens usually work @3.3V... but when you buy a
module on ebay, there are often level shifters to allow it to run at 5V. I've seen some that must be powered at 5V but the logic can be both 3V3 or 5V thank to the level shifters. You can say by looking at the PCB : are the screen's pin directly broken out or do they go through components ? A picture of the back of your screen could help.
On the modules I used, the backlight LEDs are powered by VCC (5V) and controlled by the BKL pin using a transistor. You can just tie it to GND if you want to keep the backlight ON or drive it using a pin. You can use a PWM pin to change the backlight intensity using AnalogWrite(). All that depends on the module you are using, so check twice
The .CPP (or .C or .H) files aren't opened by the Arduino IDE, but you can put some alongside your .ino file and #include them, so they will be included and compiled (it's what you do when you include a library). You will have to edit these files using an external editor, you can use your notepad, but there are better options like notepad++ or atom. Or you can use another IDE which allow to open everything (.ino, .cpp...) : there is a free Community Edition of Visual Studio and the Visual Micro plugin allows you to compile and upload your code. You can also use NetBeans with a plugin, or PlatformIO... there are plenty to choose from.