Answer:
My first is second in line; I send shivers up your spine; not quite shining bright I glitter in the light.
It is an arctic double breasted formal wear.
Everyone has it and no one can lose it, what is it?
What is the heart of many risks, has a heart, but is not a living being?
I am the greatest teacher out of them all, but alas in the end I kill my pupils.
People take me on walks and I run and have fun. What am I?