A couple of ideas and thoughts. First, adding pectic enzyme before fermentation will help your cider be clear not hazy. Also, in my experience, the cider does clear in the bottle. There could be two things going on - things suspended in the cider and haze. Time in the bottle and chilling it will help clear the cider. Haze, I'm not sure what do other than using pectic enzyme before fermentation.
Final thought - you don't necessarily have to pasteurize after bottle conditioning/carbonating. If you have let the cider ferment until its done, so that it is very dry, then add priming sugar and bottle condition, you don't need to pasteurize. If, on the other hand, you bottle before fermentation is complete, with or without priming sugar, then you need to pasteurize to stop the fermentation in the bottles before they explode.
I'm sorry i can't answer your questions about adding gelatin.