Do I still get to draw cards if I can't sacrifice Soul Ransom when its ability resolves?
Yes to all three questions.


  112.7a Once activated or triggered, an ability exists on the stack independently of its source. Destruction or removal of the source after that time won’t affect the ability.
  
  609.3. If an effect attempts to do something impossible, it does only as much as possible.


If the draw was contingent on the sacrifice, the sacrifice would be made part of the cost, or the effect would be "Soul Ransom's controller sacrifices it. If he does, he draws two cards". See Garruk, the Veil-Cursed's second ability for an example of this.