the right dpad is because you screwed in the dpad board either too tight or not tight enough
the backlight is *probably* the fuse. if not, just get a new one; you won't be fixing that without destroying the screen, thereby defeating the purpose.
the way you test is by testing a backlight you know is working on that psp. if it doesn't work it's the fuse. or you can test your backlight on a psp with a good fuse, and if it does work, it's the fuse.
theres not much need for a tutorial, just google for a picture of the backlight fuse, then either bridge it or desolder it and install a new one.