Not entirely clear in this case.
2) Does a person have a right to self-defense in one's own home?
Yes, but there is a legal duty to employ the minimum force necessary to accomplish said self-defense. In short, one does not get to turn one's doorway into a free-fire zone simply because of a perception (false or real) of illegal entry. The resident was apparently "lying in wait," ready to engage any target that appeared.
And 3) Could the actions of the police justify the actions for self-defense?
Unlikely in this case. The actions of the police officers are not unquestionably illegal, and the application of force appears to have grossly exceeded the standard for applying deadly force.
This guy's best bet is to plead diminished capacity; it looks like his pride is doing the talking here, though.