Faramir had held off the enemy for a while - long enough for wagons full of wounded to be evacuated and for Gandalf to go and lend a hand (WITHOUT Pippin onboard, unlike the film...).
With regards to the charge of the Rohirrim, it's easy to see why PJ set the action in daylight - 6000 cavalry piling into the siege lines where the only illumination is scattered torchlight or the backdrop of the burning city would be a bit dull! PJ could not have bothered with all the speeches and posturing before going forward but he's a slave to Hollywood. Theoden had no plans for the relief of the city - Tolkien implies that he was a bit stunned when he saw the scene before him, and only came to when the Witch King brought down the gates - but certainly most of the defenders had fallen back in fear from the outer wall to the second level. Only Gandalf, the Knights of Dol Amroth and a few others (brave or cut off by flames? Tolkien implies either option...) still defended the gate and only Gandalf stood in the actual gateway. It's interesting that the gate was not blocked off by stones or other barriers. The defenders seem to have given up on the idea of Rohan arriving and any sally forth was doomed to failure without assistance so why did they leave the gate without additional strength?
1. Pippin was with the White Rider in the movie so that Faramir would see a hobbit and tell Gandalf about Frodo. The PJ realized that Faramir was supposed to have a Black Dart stuck in him, so he made Denethor crazier than he was supposed to be so that Faramir would almost die.
2. I don't think that ANY of the defenders had fallen back to the second level. Maybe the boys and the servants, but that would be it. The gate of Minas Tirith was thought to be strong enough to resist anything, they just didn't count on the WK helping it along with magic. Most of the troops were on the wall raining arrows down on the enemy (and the walls were much too high for any siege towers to work). The only troops not on the walls were the Knights of Dol Amroth, because they were mostly cavalry based, so they were the only ones in the courtyard.
Why yes, I did own one of these. Back before they all became demon possessed.