Answer:
I am whole but incomplete. I have no eyes, yet I see. You can see, and see right through me. My largest part is one fourth of what I once was.
What flares up and does a lot of good, and when it dies is just a piece of wood?
What starts with a 'T', ends with a 'T', and has T in it?
I am the greatest teacher out of them all, but alas in the end I kill my pupils.
What can be heard and caught but never seen?
When is it bad luck to see a black cat?