Question: How did the reavers attack the front of the ship, killing Walsh, when they would have been behind the ship, after Walsh glided in?
Question: How did rivers fly those space ships while they are just zombies. How did they managed the whole rivers community?
Answer: The "reavers" are not just zombies, they reacted to the drug in a way that caused them to become insane. They are angry, cannibalistic, violent, hysterical. You can't communicate with them, but they can still think. They do have a society, a community. Their community is based on pillage and plunder however, finding new victims to cannibalise.
Question: Why is River bare-foot so often, especially on a ship that has a lot of metal flooring?
Answer: She has several mental disorders, presumably she finds shoes confining or uncomfortable. It's notable that when she does have footwear it's almost always heavy calf high boots, instead of slippers or more comfortable shoes.
To add; She likes to dance, and being barefoot it's easier to move around.
Answer: The reason is that Summer Glau had severe tendinitis and arthritis in her feet and wearing shoes was painful for her.
Question: Does the escape sequence at the start of the film take place before the events of Firefly, or was River captured after Firefly, and the opening sequence is her and Simon being rescued by Serenity?
Chosen answer: It is backstory, before the events of Firefly. So why does the agent only start looking for them after the events of Firefly? Mostly to give the movie a plot for audiences unfamiliar with the show.
Answer: To add to the other answer, the reason the "Operative" has only just started looking for River is answered in a comic book that was released entitled "Serenity: Those Left Behind." (The comics are all supervised by Joss Whedon, and are officially considered canonical.) In the comic, which takes place between the series and film, the "Blue Hands" from the show make their move and try to capture River, but are thwarted and killed. That's when the Alliance sends in the (much more dangerous) Operative, leading to the events of the film.
Answer: Serenity spins around as it skids across the ground...so the front of the ship is now facing the Reaver ship.
I disagree I've watched this recently and agree with the questioner. Maybe a final spin DOES occur but off-camera.
Watch the scene again (You can find it on YouTube under the title "Serenity (6/10) Movie CLIP - A Leaf on the Wind (2006) HD"), and you will see that Serenity does indeed spin around 180° and lands facing the front of the building, and thus allowing the Reavers to take the shot that kills Wash. First it bounces off a column that takes off one of its thrusters, then it bounces off another object, causing it to start to spin in the opposite direction. When the camera cuts back to the exterior a few shots later, you see it finishing a 180 degree spin and thus facing the front of the hanger. (You can even see the light from the hangar door in one of the shots).