How does the father's mental state affect the decisions he makes?

In Cormac McCarthy's The Road, the
father must overcome extreme mental and physical duress in order to survive and "carry
the fire" (keep his son alive).  The man knows he will die soon (he's inhaled so much
ash), and he faces the existential dilemma that he and his son are the only "good guys"
left in a godless universe ("There is no God and we are his prophets") filled with
cannibals and marauders.  On top of it all, keep his son's faith and spirits
high.

First and foremost, the father must deal with the
problems of suicide and mercy killing in order to protect
his son from cannibals.  Worse, the father has only two bullets in his gun: one for him,
one for his son.  But, he after he shoots a marauder, the one bullet leaves him with a
mental quandary: teach the son to shoot himself while the father fights the cannibals to
the death.  Needless to say, these options would drive anyone to mental
breakdown:

He
waited. The small nickelplated revolver in his hand. He was going to cough. He put
his whole mind to holding it back. He tried to listen but he could hear nothing. I wont
leave you, he whispered. I wont ever leave you. Do you understand? He lay in the leaves
holding the trembling
child.

In addition, the
mother has already committed suicide, and the father has terrible
flashbacks about their past life before the
Apocalypse:

In
his dream she was sick and he cared for her. The dream bore the look of sacrifice but
he thought differently. He did not take care of her and she died alone somewhere in the
dark and there is no other dream nor other waking world and there is no other tale to
tell.

Ultimately, the man
suffers from extreme paranoia: he believes the road is not
safe for travel.  He cannot tell the present from the past.  Time and again he urges the
son to stay off the road and hide in the woods.  He fears that he will not get the boy
to safety and warmer climes before his death.  Ultimately, it his son's overcoming his
father's fear after he has died and going onto the road that saves the boy.  There, he
meets the man with the shotgun and joins his family.  So, the son's faith (the very
opposite of father's mental problems) is what saves his live and
humanity.