Denethor knew about the ring, who cares how, he knew because that made the scene work, in the end it doesn't matter or effect the story. Everybody roughs up gollum, he actually tells them to stop, that's good enough for me. I didn't like Faramir in the theatrical release but the extended release fixed that.
As far as all the changes to Faramir, well there is a whole documentary on why they had to change things in Two Towers (they go in depth into the need to change Faramir in the movie and why, among other things). It is very informative on the choices they had to make as told by the people who made the changes. You really got to see this documetary if you have questions about why they changed things.
My feelings on the extended version, well I didn't like the theatric version, I don't own it, and I won't watch it again, the extended version fixed almost all my problems (and the biography on the script helped a lot too). I am thrilled to death with it. My biggest problem with two towers was I didn't care for all the jumping around and quick edits (It gave me a horrible headache the first time) the extended scenes and the added scenes makes it flow so much better. And thank goodness Fangorn got to move and kill orcs.
You got to see the documentary on disk 3 (From Book to Script: Finding the Story), I'm so glad they took the time to explain why they had to change things and the process they took.