1) You don't get extra Event cards when rolling for a Tie breaker.
Pg. 28 has a FAQ and answers this:
Q) If a 1 is rolled when ‘rolling off’ for Initiative, do
you get a free Event card?
A) No. The free Event is only if your original
Initiative roll is a 1.
2) If you choose the FIGHT option on a Danger Card, you then reap the rewards (and suffer the consequences) of the enemy you fight against. Therefore, if you defeat the enemy you get the Glory listed on the Enemy Card instead
of the Danger Card, and if you get KO'd, then you're really KO'd – No Cliffhanger.