I was wondering...

The DE sniping effects, hp attacks and the hp minusses, are any of these affected by toughness?
Can toughness absorb randomly assigned damage prior, during or after a combat?

None of the HP reductions are affected by toughness since they are not damage. Essentially at this point the only way to cancel them is to actually cancel the triggering of the effect in some fashion, though adding hammers in response may still prevent a unit from being destroyed outright.

Toughness can absorb any damage that has been assigned as it is being applied. Damage that is moved or placed is not assigned.