I remember there once being a bug very similar to what you describe with your visual bug which was triggered by NEI having to render certain boss mobs thanks to spawners. However I believe that this bug was fixed ages ago.Well thanks to this discussion I have confirmed that the mod causing the visual issues is NEI.
Yes, in the NEI options I discovered Creative+ button. I pressed it but it didn't change anything. Also, even tho I was in "/gamemode 1" (creative mode), NEI did not let me pull items from the "items screen" and place them in my inventory. Perhaps that is why Creative+ mode was suggested above, but I was unable to figure out how to activate it.
But here was my key moment of discovery. I saw NEI Options has a large button, "Disable NEI". LOL So I pressed it, and returned to my game. Guess what? No more visual glitch with the clouds, with the sun, and with the world lighting. Everything was perfectly normal! Re-enabling NEI caused the effect to return.
So I'm getting somewhere. Perhaps the answer is just to remove NEI, but that's a mod I've always felt was kind of manditory for modded, no? Since I'm having a lot of trouble with the mod, perhaps it's worth a try to remove it and see how the game plays without it.
Oh, and you can disable and enable NEI by pressing "o".
As for the being unable to pick items from the NEI menu, that is a weird one. Make sure cheats are enabled on your world and NEI is set to cheat mode.