I often have left over batter. I have frozen it for up to 2 weeks in a ziplock bag. Then just defrost in fridge and it works fine. I have also just put batter filled pans in the fridge to bake the next day. I take them right from the fridge to the oven and the result is a perfectly level cake.
You may leave your batter in the fridge and not worry about a thing.
I have never heard of CC icing curdle. If it's your basic recipe (room temp CC, butter mixed with powdered sugar and vanilla) there is no reason why it should curdle. I agree with scrumdiddlycakes, maybe you have under mixed it?
Here is another one I did this weekend. I printed the zebra on whole sheets of Icing Images white paper. I was afraid to use the Wilton pre printed sugar sheets because they are thinner, All decorations were made from gumpaste.
ellavanilla I did another one this weekend and I should have shot a few pics but I didn't! I promise I will though next time. I have a person interested in one for August. I have never used IMBC but I'm sure this would work in it.