Problem 1. There are 10 possibilities for the cards not hit by the snare. (AB, AC, AD, AE, BC, BD, BE, CD, CE, DE). Let's say arbitrarily that IHW are A and B. If neither or both are hit by the snare (AB, CD, CE, DE), you're guaranteed to survive. So there is a 60% chance of only hitting one, which leaves you with 5 cards in hand. Now two meat damage is applied three separate times, and only if the first two iterations miss the IHW do you die. 1/5 chance of that happening, so 1/5* 6/10 = 6/50 = 12% chance of dying.
Problem 2: There are 9 cards you want. Odds of whiffing on a hand are (31*30*29*28*27)/(40*39*38*37*36), or approximately 25.8%. Odds of whiffing twice are .258^2, or 6.6%. Edit: 6.6% is the chance of NOT starting with one of the desired cards. So the chance of starting with the desired cards is approximately 93.4%. With a 45 card deck, that probability drops down to ~90.5%.
Bonus: There are now 35 cards in the deck, and you are seeing three of those. 26 of them are cards you don't want to see. (26*25*24)/(35*34*33) = 39.7% chance of whiffing, or a 60.3% chance of seeing what you want off the Diesel.
Edit: spoiler tag