Ok Ill give this a shot. First dealing with your error 002 problem. Those games that give that error have 1 of 3 iso's. They are either 38,53 or 55. To determine what iso number a game uses, download iospatcher and open the ios file using iospatcher. Anyways, theres 2 ways to fix that error. You can either go and install those 3 iso numbers onto your wii (yours currently arent installed or arent up to date) or you can patch the game. I go and patch all my games that have any of those 3 numbers just to be safe. To patch, youll need to download wiiscrubber and Bailli's generic wii patcher. If you go that route, simply PM me and ill walk you through it. make sure when you download wiiscrubber, that you get the included key.bin file or else the program wont work.
Your problem with mario kart youll need to give me more details on it before I know what the problem is. I "think" 60hz deals with pal games so if its a pal game, thats the reasoning. Let me just say that if you are using an out of region game on your console, try not to. That could be the reasoning for your mario kart problem. And it could be your reasoning for your other 2 games you mentioned giving a black/white fuzzy screen. When you play a pal game on a ntsc console, dont change the region using regionfrii, and dont force NTSC in configurations (when using backup launcher) youll get that problem.