tolkiens legendarium - Are the events at the end of the Two Towers film consistent with the film's internal plot?

First up, let me be clear this isn't a purist's question. Books are books and films are films and both should be considered on their own merits.

However, every time I watch the film version of The Two Towers, the events at the end of the film regarding Faramir and Frodo annoy me, not because they've been drastically altered but because those drastic alterations don't seem to make sense, even within the film's own version of the story.

A warning for all the people who haven't seen the film yet: major spoilers follow.

Here's what I find problematic:

First, Faramir's aggression and (worse) the cruelty his men inflict on Gollum, stand at odds with the picture painted elsewhere of the men of Gondor as wise and just. Not only does this jar when the characters are introduced, but it lessens the viewer's sympathy with the people of the white city in the travails that are to come.

Second, there doesn't seem to be any good reason why Faramir doesn't simply take the ring off Frodo and bear it to Minas Tirith, alongside his captives. Given that the film has established Faramir and his troops as being fairly ruthless, and that Faramir makes light of the corrupting power of the ring, this seems an odd choice.

Third, and most difficult for me, is Faramir's motivation in letting Frodo go. He chooses to do that after watching Frodo almost become enslaved to the will of a Nazgul, underlining, surely, that Frodo is not fit to undertake the perils of bearing the ring into Mordor. How does this demonstration of powerlessness convince Faramir that he is wrong in bringing the ring to his father, and that it's actually safer in Frodo's hands?

The crux of my question is this: have I missed something in the films, or is there interview material elsewhere, that help make sense of these apparently bizarre plot points so I can enjoy the film in the future without them bugging me?