Answer:
I have one, you have one. If you remove the first letter, a bit remains. If you remove the second, bit still remains. If you remove the third, it still remains.
I am the greatest teacher out of them all, but alas in the end I kill my pupils.
Of these things - I have two. One for me - and one for you. And when you ask about the price, I simply smile and nod twice.
What has 13 hearts but none beat?
Take one out and scratch my head, I am now black but once was red.
I have two eyes in the front and a lot of eyes on my tail