Answer:
Cold head and feet; round as a ball; always turning around myself.
I can be found after you remove 6 letters from BSAINXLEATNTEARS
Four leaves I have.
I always follow you around, everywhere you go at night. I look very bright to people, but I can make the sun dark. What am I?
I am a kind of coat that can only be put on when wet. What am I?
Almost everyone needs it, asks for it, gives it. But almost nobody takes it.