1) Right, so it is about scavenging but the focus isn't so much on fighting the zombies as surviving them (there is a bit of a push to sneak about, not make much noise, only engage small numbers, etc), which in my opinion makes it much more interesting. You do have guns and melee weapons, as well as explosives and some typical urban vehicles, but don't expect to be able to go rambo on the undead. Depending on the character you play as, you may not have enough stamina to even swing a machete before getting tired. There are other groups of survivors who you can trade with and will give you the occasional mission (help them enough and they may ask to join your group), but there are no hostile humans.
2) Yes and No. You don't get to choose cloths, hair-styles, etc. You can play as (mostly) any character in your group, each with their own set of skills, weapon preferences, traits, etc. As you use them more, they become more powerful (running will increase stamina, shooting will improve that skill, etc) and every so often you get to select a perk that helps with combat or scavenging (quicker takedowns, quieter searching, etc). You can also customize the loadout of the survivors in your camp so they can stand a better chance if a zombie makes its way in the camp when you're not around (but the AI is a bit dumb with guns if I remember). With the Breakdown DLC, you can also unlock unique survivors to play as from the get go.
3) Yup, kinda. You're character will get tired (temporary drop in max stamina and its regen rate, you'll need to switch to someone else while they rest), injured (needs to rest and may need a doctor), or your camp will be under siege from the hoard and you will need to go and help (the group may overcome it alone, but you may loose someone important). The game really focuses on working together.
4) A good size for the game. It can be broken down into the more rural eastern zone with a small town, the large farmland in the center, a small city in the west, and a somewhat dangerous northern zone featuring an amusemant park and some office buildings. It's large enough to not feel too constrained, but you will always feel the need to be conservative with your resources as they don't re-spawn and you'll start to see the "X"s on the map (denoting a cleared/drained area) stack up fast. It's open world as well. Vehicles are fine, if a bit arcade-y. The Lifeline DLC was set in the larger city to the north (you can see it in the base game, but can't go there). It has a bit different gameplay and is MUCH more dangerous.
5) I'm really not sure. I imagine a disk?
6) The base game has a story and an ending. The Breakdown DLC is the basegame with no story and a mechanic where you can...well...I'll explain the DLC below.
DLC 1 - Breakdown.
Great DLC. You start by selecting on of like 30 characters (most of which need to be unlocked first) and you're dropped in the world. As you build-up a base and a community of survivors, you hear over the radio that there is an RV somewhere. You find it, repair it, and can then select what you want to take with you (resources, characters, whatever) but you have a limit. It then basically resets the map with more zombies and fewer resources. And the cycle repeats.
DLC 2 - Lifeline.
Not my favorite, but still pretty good. You are a commander of a team of soldiers charged with wrapping up in the city before being evacuated. You get missions to rescue VIP's, secure resources, etc. You are also dealing with a constant countdown that, once it hits zero, sends and massive siege at your base (and I mean massive). The map is smaller, but has a lot of nooks and crannies to look in, and the timer keeps you always on edge. You can get air support, mercenary assistance, and supply drops every so often to help out. You'll need it.
The "sequel" is a proposed MMO currently called Class-4. But with the flood of zombie MMO's and zombie games in general, I don't know if they are still going to go the MMO route.
If you couldn't tell, I very much like this game. If you have anything else you'd like to know, I can go in more depth.