Answer:
My first is equality; my second is inferiority; my whole is superiority.
A skin have I, more eyes than one. I can be very nice when I am done.
I dig out tiny caves and store gold and silver in them. I also build bridges of silver and make crowns of gold. They are the smallest you could imagine. Sooner or later everybody needs my help. Yet many people are afraid to let me help them.
I'm tall in the morning and short in the noon. I disappear at night but I will be back soon.
I always run but never walk, I sometimes sing but cannot talk, No head on which a hat to place, You always look me in the face.
I am black within and red without; with four corners round about. What am I?