If a creature has first strike and another has deathtouch, say the first striker attacked the deathtouch, would the deathtouch kill the first striker in first strike combat damage, after damage has been applied?
Creatures can only attack players and planeswalkers, not other creatures.
Deathtouch only works when the creature with deathtouch deals damage. If the deathtouch creature is destroyed during the first strike combat damage step, it won't deal any damage, so deathtouch won't apply.
Deathtouch is a static ability that modifies the way a creature deals damage. A creature without first strike or double strike does not deal damage in the first strike damage step, so deathtouch is irrelevant. Assuming the first strike creature has a high enough power, the first striker survives and the deathtoucher dies.
It totally would. Something like Glissa, the Traitor will deal damage in First Strike damage step, which is before the Normal damage step. Assuming the creature it battles doesn't have protection/doublestrike/first strike/is indestructible, Glissa will deal lethal damage to it, and kill it before it can hit back.
Misread the question, my bad. See the above answers.
Deathtouch means that damage the source deals causes the damaged creature to be destroyed. If a creature doesn't have first strike, it doesn't deal damage in the first strike combat damage step. It'll only kill the first striker if it lives through the first strike combat damage step and deals damage in the regular combat damage step.
If you block an Ambush Party with an Acidic Slime the Ambush Party will deal 3 damage to the Acidic Slime in the First Strike Damage Step. This will kill the Slime before you move to the normal combat damage step so the Slime will not deal it's damage to the Ambush Party.