I wouldn't use the word "discovered" it just seems a bit off. I'd rewrite the sentence with a simpler word yet easy to say and understand: "When we searched the school for damage, a new broken window was found." I hope this helps you. My apologies if this is incorrect.
Answer:
no, we cant say "could have HAVE been"
Explanation:
saying double have sounds weird and isn't the right way to talk.
Answer:
b) the "will work for air conditioning" sign,
c) the rat sweating on the sidewalk,
e) the comfortable man in the air-conditioned car
Explanation:
See attached image