Leaving it on it's lees for a full month won't hurt it, so you're fine. When making a dry cider I like to wait until it is completely fermented out before racking to the secondary. The reason being that if you rack to a secondary and there is still yeast activity, that yeast will then die and sit on the bottom. You can
get off flavors from autolysis but I wouldn't worry too much about it in any case.
It may sound funny but kicking, rotating, or moving the primary fermenter will jar loose some yeast and sometimes gets the fermentation going again. I wouldn't shake it though.
I'm not sure what yeast you used, but the temperature does play a good deal, as well as how well you aerate. Just the old standard brewing rules apply there.
As far as adding stuff to your cider, nutrient works great. It also helps keep down any rhino farts. Yeast energizer will also help speed up your fermentation.