Blocking and instants.

[Galabranth]

So lets say my opponent taps his dude to attack. I decide to block it with my dude. Without any intervention, both should die. However, he does a Far/Away and does away with my dude. Does the damage my dude deals to his dude push through?

[Tonygrabowski4]

No.  As your "dude" is not there for the combat damage step.

[Galabranth]

Without Apathist everyone gets to answer quick. Both happy and sad.