1. I don't have a weapon in play. Can i still use abilities like sinister strike and backstab to do damage? The cards say do X+1 and X+3 damage where X is the damage of your weapon. If i don't have a weapon that should just make it 0+1 or 0+3.

2. If the preceding works, could i use cold blood, then sinister strike to deal 1 damage to something to kill it without having a weapon in play. Say my opponent puts Moko Hunts at Dawn into play, and i want to cold blood then sinister strike to kill it before it could attack.

1. Yes that would absolutely work, because technically your hero does have an attack, it is just 0 (zero). You could exhaust your hero to attack an opposing ally or hero, if you wished, but you would deal 0 (zero) combat damage to them (given that you don't have any +ATK modifiers)

2. Yes, that would also work, because "Cold Blood" states that your hero needs to be the one doing damage, and "Sinister Strike" states that your hero is the one doing the damage. Notice the relation there?

Now, this would be different if "Cold Blood" required your hero to deal combat damage instead of just damage. In that case (combat damage) it would not work. I hope I didn't make this too complicated!