Two: The world is half-dead. No green plants or flowers ever grow, and the sky is perpetually gray. Volcanic ash often falls from the sky in a twisted parody of snowfall. It gets everywhere. There is agriculture, but it generally focuses on grains and mushrooms.
Three: The world is in a strange pseudo-medieval stasis. Technology hovers around... the Elizabethan era, I'd say. Gunpowder exists, but it isn't widely used at all. There are, however, 19th century-style canals. (Also, I believe formalwear is fairly modern, but I may be wrong on that).
There are Nobles, and there are Skaa (essentially a serf caste). The noble houses bicker and maneuver, and the Lord Ruler tolerates that. The nobles also have the magic, which is at least partially hereditary, in their blood. The skaa's lives are worth little to nothing, breed like rabbits, and are technically owned by the Lord Ruler, who parcels them out to the nobles as a workforce.
Both castes are human, I should point out, and enough (illegal) interbreeding has gone on that it's not uncommon to see a skaa with a minor magical talent.
Fourth: The magic. This is expanded upon in the books, but since this is a prequel, I'll stick to the basics.
The magic is called Allomancy. It works by ingesting small pieces of metal, and then using the different metals to fuel different abilities. The commonly known abilities are:
Pulling- by eating Iron, you can Pull anything metallic towards themselves. Physics still apply, so if you pull something heavier than yourself, you will move toward it instead.
Pushing- by eating Steel, you can Push anything metallic away from themselves. Physics still apply, so if you push on something with more resistance than your weight, you will move away from it.
Tin- by burning Tin, all of your senses become greatly magnified.
Pewter- by burning Pewter, you become stronger, tougher, and faster.
Zinc- by burning Zinc, you can enflame the emotions of those you target.
Brass- by burning Brass, you can calm the emotions of those you target.
Note: Canonically, there is little effective difference between the two emotional metals. That is, if you want to make someone angry, you can either enflame their anger, or calm all of their emotions BUT anger.
Bronze- by burning Bronze, you can determine if others are using Allomancy and, with practice, which metals they are burning.
Copper- by burning Copper, you render yourself immune to Zinc and Brass, while also generating an invisible field that hides you (and those around you) from Bronze burners. Those around you do not gain protection from emotional elements.
Gold- by burning Gold, you can see what you might have been if you had made different choices in the past. It is rarely used due to possible severe emotional trauma.
Electrum- (minor spoiler, but relevant so I'm including it). A person burning electrum makes their actions impossible to predict, thus negating atium's ability.
And, the big one...
Atium- by burning Atium, you can see a few seconds into the future, thereby allowing them to anticipate the moves of an opponent. A Mistborn burning Atium is effectively invincible.
However, atium is very rare, and is burned very quickly, making it the most valuable metal in the world. It is mined in small "beads."
As for that word I keep using, "Mistborn..." Mistborn are the (very rare) individuals who have access to every power I just mentioned. The (still rare, but more common- I want to say 8% of the population? Book 3 gives a percentage, I believe) Mistings are those who are able to only burn one metal.
Fifth, and final: The religion. The only known religion is that of the Lord Ruler, who runs it more like a government than a religion. His priests are known as Obligators, and they are his eyes and ears. Additionally, (and brilliantly, if you think about it), they are effectively super-notaries- it is both a culturally and legally accepted truth that no deal is final and official unless witnessed by an obligator.
There is another branch of the obligators- the Ministry of Steel. They are staffed by Inquisitors, giant warriors with iron spikes pounded through their eyes, merciless, and equipped with many powers, both Allomantic and unknown. Their primary function is to root out and Noble/Skaa pairings and their offspring, but they are so deadly that they are used for other tasks, as well.
Phew. I think I hit most points. Any questions or additions?