I've never bothered removing the skin from the chick peas, simply because it's more work than I'm willing to do. I have no doubt though that, without the skins, the hummus will have a smoother texture.
I like to keep it in the fridge for a day or two. That makes the flavours blend more, and also improves the texture as the moisture makes its way more evenly throughout the chick peas. I also found that, over time, the mixture becomes more firm. When first blending everything and adjusting water content, I tend to err on the slightly runny side; a day or two later, all the water gets absorbed and the texture is just right, without being too firm.