Answer 1:
If you don't know anything about the impedances I would always use series termination in the range between 50 and 100 ohms. Which value you choose is not that critical, but as a rule of thumb: When the communication still works with a higher value, choose that. EMI is caused by reflection due to impedance mismatching. The intended Signal will have to flow through the series terminator only once, whereas a reflection will have to do this at least twice causing it to shrink. So series termination is no reflection prevention but an effective and easy way of reducing it.
Don't try to attach an oscilloscope to evaluate signal integrity, since this will significantly influence the signals.
Answer 2:
The frequencies you mentioned can be suppressed using ferrite beads. If space is no constraint, try the one you can wrap around FCC cables.
Power lines should be buffered with capacitors on both boards, make sure to use caps that are fast enough. It is common practice to parallel multiple caps (say 3x100nF) to reduce ESR.
If you still have problems with the clock you can try to add a low-pass at about the clock frequency before feeding it to the cable and restore/buffer the clock at the sink board if necessary.
Looking at the SetXY function, it seems the controller might be ILI9341. Here's a datasheet for that controller:
http://www.newhavendisplay.com/app_notes/ILI9341.pdf.
There's two points that strike me at this time; hopefully as new information becomes available, I can extend the answer.
First of all, are the definitions for SCREEN_WIDTH, and SCREEN_HEIGHT correct? It looks to me like they might not be.
Secondly, what pixel data format, e.g. how many bits per pixel, do you set for the LCD. Usually these kinds of LCDs accept data in formats such as RGB565 (16 bits per pixel), BGR233 (8 bits per pixel) or RGB666 (18 bits per pixel). The code for DrawPixelLine suggests that the data is 8 bits per pixel; in my experience this is quite rare, although the striking thing in your image is that the colors seem to be correct. Having the wrong pixel format would explain a lot.
It's rather odd that there seem to be two different entities for the screen height: SCREEN_HEIGHT and disp_y_size. Are you sure both are correct?
Edit: Based on the ILI9341 datasheet; that controller doesn't support 8-bit pixel depth. Also you declare your data buffer to be of type u_int16. However, in the line draw function, that buffer is cast into an array of char. And I think that in the Arduino (AVR), a char is 8 a bits data type. This would cause incorrect indexing to your data buffer.
Best Answer
The backlight has a rating of 20,000 hours where at that point the backlight should be 50% of original brightness.
I can't get any information on pixel lifetime.