Answer:
I am a kind of coat that can only be put on when wet.
Born of sorrow, grows with age, you need a lot to be a sage. What is it?
I fly when I'm on and float coming off.
I have a little house in which I live all alone. My house has no doors or windows and if I want to go out I must break through the wall.
I am a certain five-letter word and become shorter when you add two letters to me. What am I?
No matter how little or how much you use me, you change me every month.