You're going at your problem the wrong way. You don't need to capture a Demon or Forgotten Beast in a cage trap to start a silk farm - all you need to do is trap it in an area such that it can shoot its webs but not otherwise bother you.
Mitchewawa on the Bay12 Forums has quite an extensive topic on this very subject.
The crux of it involves exploiting pathing and the fact that building destroyers cannot destroy hatches from below. Basically, you want to isolate your webber, then use caveins etc. then dig out a silk farm area based on where you isolated it, and finally, sacrifice a migrant to get it into the silk farm area (with the possibility of orchestrating a cave trap to seal it off again).
Ok, I am going to attempt to answer all of your questions one at a time.
First of all, you wondered about clothing and arming your dwarves. While is does become a problem at some point, it doesn't usually for a while, you have at least enough time to buy cloth from the merchants (they always come with a ton) and build a couple workshops. Arms-wise, you should only have weapons in use by your military, and you shouldn't need a ton of military dwarves, it is always most efficient to have your defenses based around traps.
Secondly: bedrooms. I have found that it is best (until you reach the population cap, although that tends to be a bit buggy) to have all of your dwarves sleep in one giant dormitory with many beds. You can do this by building a bedroom that encompasses all of the beds in the area and then toggling "dormitory" to "Y." This way, you have one area where all of your dwarves sleep, and the only thing you will need to worry about is having enough beds. You probably only need the number of beds to be 25% of the number of dwarves you have, as that should cover all the sleeping dwarves. It is even better to have a much larger room with half of it being a statue garden, as then you will have dwarves in the room who are awake and will see it if any vampires start killing dwarves.
For pens and pastures, there isn't a great way to make them efficient that I have found. There isn't really a great need to have them, though, because you can buy a lot of cheese and cloth from merchants. The only reason you would need a pasture, I've found, is for a chicken egg-laying area, but for that, you can make it underground in stone, you just need to be sure to have nest-boxes.
Building configuration-wise, I find that it is good to have a set plan for design before-hand. For example, know that you will put a lot of your workshops in one area, and your meeting hall and bedroom (see above) in another. It's also good practice to only dig out enough room for the workshop and not to group them all together in one room. You should also have rooms for your stockpiles near the corresponding workshops. Also be sure to have one "main" hallway, it should be 3-wide or more, as this will prevent traffic jams down the road.
Finally: farms. I would recommend you build a couple plump-helmet farms, as large as possible, to feed your dwarves. Seeds shouldn't be a problem, just go to the overview (z) menu, move over to kitchen, and disable plump helmets for cooking but not for brewing. You should have several breweries to make alcohol, and these will also return seeds. It is also good to have an egg-laying center (see above) and a kitchen. Hens and roosters will produce a ton of eggs, and if you set your kitchen to auto-repeat cooking easy meals, you should be able to feed your dwarves.
Best Answer
What Did You Kill?
First of all, what is it you're trying to butcher? Dwarves will only butcher non-sentient creatures (unless you edit the raws).
The title of the question asks about a forgotten beast, which is non-sentient and therefore butcherable, but the body asks about a were-chinchilla, which is a type of night creature. Unfortunately, night creatures are sentient and cannot be butchered.
If you did kill something non-sentient, keep reading to find out how to turn its bones into awesome crafts.
Getting the Bones
First, if the forgotten beast was killed outside your fort on the surface, your dwarves won't collect and butcher the corpse unless you allow refuse collection from outside. To do that, press o to open the Standing Orders screen → r to open Refuse → o to allow Dwarves Gather Refuse From Outside
Next, ensure that you've built at least one Butcher's Shop (workshops → Butcher's shop). If you have at least one dwarf with the Butcher skill enabled, the beast will eventually be cut up into its components.
Congratulations on obtaining some forgotten beast bones! To turn them into crafts, you have two options:
Option 1: Custom Stockpile
Option 2: Work Order
Enjoy your dwarfy new forgotten beast bone mug or whatever!