On Denethor: I get the feeling that he was a hard, stern, cold man - sort of like the stereotype of a 'Puritan'. He was often unreasonable, demanding things that he had no right to ask for. Probably his only soft spot was for Boromir, and once Boromir was dead... but it doesn't excuse his dereliction of duty. For a descendant of Numenor he sure didn't understand the idea of resisting evil to the last very well. As I see it, he gave up when it seemed all hope was lost.
For a man as "far-seeing" as Denethor was reputed to be, he was pretty blind to ideas that fell outside his experience. Like Boromir, he thought in terms of power as a weapon, we see that he expected his son to bring the Ring to him, as a weapon. I think that because for such a long time Gondor had held Mordor back by physical strength, strength became all that they could understand. The Northern Dunedain, the Rangers, also used physical strength to oppose evil, but they had the example of the Elves to show them that there were more kinds of power in the world, and that power should not be taken lightly.
Faramir, I think, understood that idea because he spent time with Gandalf. Hey, maybe those seventeen years while Gandalf was researching the Ring weren't entirely wasted! We could postulate that Gandalf was 'cultivating' Faramir all along, probably saw him and his brother and father for what they all were and knew Adequate was the best of the lot.
I'm using a Gone With the Wind illustration again, but when Scarlet's mother died, her father lost his mind. At Gerald's funeral, Will Benteen described his descent into madness as "his mainspring busted". There was nothing on the outside that could lick Gerald, but it was from the inside that he could be destroyed.
Anyway, Denethor's world must have fallen apart since Boromir was his "jewel". But that doesn't excuse his treatment of Faramir, and it doesn't excuse his retreat into the death house instead of leading the army into battle.
Denethor's grief is evident when he diminishes Faramir in front of Gandalf. It shows much of Faramir that he didn't punch his father in the brain, but went out to do battle for Gondor.
The blood of Numenor was thin by Denethor's time--but even Numenor had it's losers. That little twip Ar-Pharazon, to offer a prime example. Two of the great failings of Numenor were pride and fear--vices Denethor, in large measure, inherited.