[H. Have You Heard of Cricket?] In calculation of NRR, do we count only valid balls?

Yes.

[H. Have You Heard of Cricket?] Is it possible to score 8 runs in a bal? Suppose it is a no ball..

At most 7 runs can be scored including no ball.

[F. Elevators] Is the explanation correct?

There is an error in the PDF of problemset. Please see correct explanation from description in CodeMarshal.

[H. Have You Heard of Cricket?] if in the first innings, total score is 0 and in the 2nd innings..