I have no idea why you would set jobs with the normal UI instead of DT. Unless you're a masochist. Are you a masochist?

Oh yeah, and I can't bury the dead because I have no idea how to make coffins, so they're sealed up in a room.

Hunters need crossbows and arrows, and it also seems that in the newer updates they need quivers as well.
Craftdwarves can make wooden or bone bolts, and a Bowyer can make crossbows out of bone or wood too. Quivers are made of leather iirc, which would require a leatherworks and suitable dwarf for the job. Unfortunately, leather would require dead animals, of which you have none but I'll get to that later.
The reason your hunters are hunting rats and other vermin is probably because you don't have any food, bolts, quivers, or crossbows - or maybe all of the above. As a result, they're eating vermin to survive (they'll have a note about that in their status menu).

Here's a step-by-step on how to try and resolve your problems with your fortress before it goes under:

1) Farming. You'll need to make a farm plot, one above ground for normal plants, and one below ground for mushrooms such as PLUMP HELMETS. Plump helmets are great because they provide both a source of alcohol and food in one tasty little morsel. Make sure to use "q" to set the plants which are to be planted. Your farmers will get onto it sooner or later, provided you've set some dwarves for farming.
1a) It helps if you "d"esignate an area for dwarves to "gather plants" so you'll have a good supply of booze-yielding plants and seeds available.
2) Booze. Once you have sufficient alcohol-making plants available, go to your still (it's a workshop, so press "b", then "w", then "l") and set it to brew a drink. You'll always need barrels to keep the stuff in, so make sure you have a carpenter on that or you'll have no booze at all. Keep in mind that just about any plant can be made into alcohol, and that dwarves don't like having to drink the same stuff for too long.
3) Hunting. Since your hunters are apparently ill-equipped, the next best thing is to set up a "m"ilitary. Chuck a couple of dwarves into a squad in the military menu (preferably ones with some combat skills - it'll tell you under "relevant skills") then go back to the main screen, press "s" for squads, "a" to select your first squad, and then "k" and "l" to get a list of things to send them out to kill. There'll likely be some harmless animals milling about outside, so send them after something less dangerous like hoary marmots or elk. With time, they'll be able to hunt down and kill something for you - just remember to cancel the kill order once they're done or they'll just sit around the carcass like tentative vultures until they starve to death.
4) Butchery/Cooking. The first and most important thing to do is to go into the "o"rders screen, then "r"efuse, and then allow your dwarves to collect corpses from outside. Make sure you have both a kitchen and a butchery set up, and a corpse stockpile (corpse under the refuse list in the stockpile settings, not the "corpses" listing by itself) nearby. You'll want to either build the butchery and corpse stockpile together above ground, or below ground and far away from anything else with air vents dug into the roof above (channelled using the designate menu). Once you've got the butchery and corpse pile set up, and a dwarf set for butchering then your butcher will automatically set about butchering any animal corpses nearby. This will provide food for your cook to prepare. Now all you need to do is go to the kitchen and set it to prepare a meal. I like to stick the kitchen on "prepare fine meal" and set it to repeat.
5) Equipping your hunters. Now that you have corpses being butchered, you'll have some skin sitting around. If you have a tannery set up, your tanner dwarf will take any skin he can find and turn it into leather. Once he's done, a leatherworks and leathermaking dwarf will let you produce quivers (and armor!) for your hunters. The crossbows and bolts can be made out of the bones you'll have from butchered corpses (or wood), and all you need is a bowyer's workshop and a craftsdwarf workshop, and of course dwarves set to the task. From then on, your hunters set to the "hunting" job will set about shooting down and retrieving animals. It's also helpful to set used ammunition as collectable in the orders menu if you don't want to be wasting resources on bolts.
6) Burying the dead. Since you're having problems with that, all you need to do is have caskets or coffins made by either carpenters or masons. Then have a room underground somewhere where you can build the coffins. All you need to do after that is to press "q" go to the coffin and set it to be available for burial. Another thing you can do is have a mason build a slab and a craftsdwarf engrave it. Both ways should prevent ghosts from rising and tormenting the living.

Hopefully that's all correct and will fix your problems - provided you work fast enough before your dwarves all starve or start having tantrums. If those insane dwarves are still around killing people, try to lock them in a room with a door by forbidding passage through it. Otherwise you could send a couple of military dwarves after them - they shouldn't be too much of a threat.


As a side note, I use the default interface for dealing with jobs, and yes it is a long and arduous process, especially with migrant dwarves who seem to need help deciding that they should put their "Skilled Fisherdwarf" skill to use in a fishery rather than just sitting around eating food, drinking booze and generally acting like mobile fortress cancer. I think I'll be getting that Dwarf Therapist thing soon.

Coffins are made at a mason's workshop. Then once you construct them, you need to set them to be available for burial, and one of your dwarves will inter the body automatically.

Okay, thanks, this helped quite a bit. But I had a squad set to defend the above ground from crazy wolves, and that's when 2 of the soldiers snapped. They killed almost the entire squad before I could bring them down, and so I have a couple of stable spearmen guarding the fortress and acting as police, but my main problem now, is the hospital. The dwarves with broken skulls just waltz into the hospital, lie on the bed, and then they end up dying a week later because my doctors won't stay put.

And my best ranger has a shitton of copper bolts (I'll build wooden supplies for the others in a bit) but he can't comprehend the thought that killing an elk is better than stepping on a rat. :/
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Oh, okay. I was trying to find them in the carpenter's workshop. Thanks.
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And so far my dwarves are living off the plump helmets I brought from home, which should give me some time to get my shit together.

Carpenters can make them too, it's just that they're called "caskets" instead of "coffins".
As for that hunter, you could always just set him as being his own squad and send him to kill them elk :P

Also, another good way to save your fortress from starvation/thirst it to steal an entire caravan by deconstructing the trade depot when the caravan's sitting on top of it. I try not to do this to the dwarven ones though. Elves are easy pickings.

As for hospitals, I have no idea how to get them working properly. Best bet would probably be to stop the healthcare dwarves from doing anything but their healing jobs, and set them some rooms alongside the hospital. Having a water source available should also help.

Oh wow, my doctor's and field medics are finally doing their job now that they know I can provide food

And my hunters are finally killing things that aren't rats, and they're still using copper bolts, but I'll make wooden ones just incase.

The only problem now, is that one of my fisherdwarves went crazy

Wooden/bone bolts are pretty low tier. I only use them for hunting because you can mass-produce them. Copper and other metal bolts should be reserved for marksdwarves IMO, but hey, they're providing food so no reason to stop using them now.

You can also have a craftsdwarf make bone armor for your soldiers, which is decent until you get a nice supply of metals and have your smelters and forges set up. Bone somehow comes under "Metal Uniform" on the military menu.
Hunters could probably use some decent armor too. I've had a few of them who were stupid enough to try take on giant hamsters and the like and have their limbs removed.

As for that fisherdwarf, have him killed. No one will miss him, hopefully.

Well, the fisher dwarf killed a certain beloved puppy, so I beat the shit out of him.

and this is the main section of my fort




I'll build more caskets next.
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Any tips on how I can make my whinny-ass sheriff actually enforce justice on these people?

There's a justice menu somewhere, don't quite remember where. Probably "j". Anyway, you need to build a room with cages and set it as a room like what you do for bedrooms or dining rooms.
Oh, and to convict someone, a dwarf needs to have reported a crime to the sheriff, along with who he's accusing. Be warned that if you have a vampire in the fort, they'll counter-accuse whoever caught them just to make things confusing for you.

The convicted dwarf will likely be sentenced to a certain amount of hammer strikes by the hammerer.
Also, have you made the appropriate rooms for your sheriff? Check the "n"obles menu. If he doesn't have all his required stuff, he won't do his job and probably get pissed off.