If my creature with deathtouch and 0 power blocks one of my opponent's creatures, does my opponent's creature die?
No. Deathtouch still requires that damage be dealt:


  702.2b Any nonzero amount of combat damage assigned to a creature by a source with deathtouch
  is considered to be lethal damage, regardless of that creature’s toughness.


Here's the more general rule as well:


  119.8. If a source would deal 0 damage, it does not deal damage at all. That means abilities that trigger
  on damage being dealt won’t trigger. It also means that replacement effects that would increase the
  damage dealt by that source, or would have that source deal that damage to a different object or
  player, have no event to replace, so they have no effect.


A corollary to all this is that a creature with deathtouch can only kill as many creature as it has points of damage to assign -- for instance, casting Lure on your 2/2 Acidic Slime doesn't let you wipe out your opponent's whole team, just two blockers.