Bad toss and rejump - the clock.

[Hawks Coach]

5-9-2
If play is started or resumed by a jump, the clock shall be started when the tossed ball is legally touched.

If the toss is bad, ball is not live and it is not legally touched, therefore clock doesn't start (or shouldn't). That's why I say re-set on first condition I outlined - obviously subject to debate.

As for starting in the second case, it seems clear to me. Ball was legally touched, clock starts on tap and stops on whistle. That's how the rule reads (stopping is in 5-8-1, and it is when official signals a violation, not when violation occurs).