If I format my 3DS, will I still be able to play software saved on an SD card?

Hello,

Thanks to some genius from Nintendo who repaired my 3DS, I'm no longer able to use my NNID on it (Err. #022-2501) and I've come to the conclusion that I'm going to have to format my 3DS to fix the problem. I currently have Pokemon X and a few other titles saved to my SD Card, will I still be able to play them after I format my 3DS and possibly have to get a new NNID? Or will I have to purchase them again? Will I loose all my Miis?I also have some 3DS games on actual gamecards. Will I lose any data needed for those?