Hi Connor, welcome to the forum! I'm sure you'll find a lot of help with your challenging project here.
Your machine is a really nice find, for all its problems, and while it'll take a lot of work and a decent amount of cash to make it good again, it's well worth the trouble. As you know, the leather-front version doesn't turn up that often.
To address your questions in order: there's a very good tutorial by the estimable "chilldude2007" on restoring the dashpots on YouTube:
https://www.youtube.com/watch?v=QKHdzIL0mLU -- he walks you through all the steps required to make them work properly again, and I found this video really helpful when restoring mine. A first thing you might try, though, is letting a few drops of neatsfoot oil (available from a shoe repair shop, or online) slide down the bar and into the tube of the dashpot. There are small leather disc-like cups inside that are meant to control air pressure. Often these have dried out and can no longer do their job. Neatsfoot oil (which was what Victor recommended for the job)may be enough to make these supple again. Don't overdo it; start with a half-teaspoon or so, let it sit overnight, and see if it makes operation better. Add a little more oil next day if the first try doesn't help. If this doesn't work, the video shows how to reverse the direction of the leather discs. That's what ultimately worked in my case.
Rayon-covered lamp cording is available here:
http://www.antiquelampco.com/Catalog/Cord.htm
The bun feet are a big problem with a lot of these machines. When exposed to moisture in damp basements (and it sounds as if "moisture" is an understatement in the case of your machine), they tended to split and fall apart. Intact examples come up from time to time on eBay, some of the sources for parts in the forum's "links" section (which should be very useful to you as you proceed with restoration) may be able to provide them, or a request in the forum's "Yankee Trader" section may turn them up at a reasonable cost.
I'll leave it to others to address the availability of the vent grills -- I seem to remember that OrthoSean had suggestions in another thread about them, and other members can probably suggest good sources as well. Folks who know more than I do about electric motors will probably recommend servicing before you run it at all, for safety's sake.
You've got a lot of veneer issues to correct, and these may be somewhat difficult given the condition of your machine. Veneer was typically applied with hide glue, which is a little more labor-intensive to work with than today's carpenter's cements; but it's also easier to correct. It's sensitive to heat and moisture, and if you're unable to relaminate the veneer in its current place, you should be able to remove and reposition veneer by applying heat with an ordinary clothes iron, and relaminating it. This isn't hard to do, but it has to be done carefully or you're back to square one. In some cases you'll be able to inject glue where needed under veneer that's partially loosened with a small syringe.
Regarding the musty smell, sunlight, air, a good cleaning, possibly some baking soda, and time should make it tolerable.
I think (though I'm not 100% certain) that the leather panels were probably adhered with hide glue as well, and could be re-adhered in the same way that you do the veneer. If there's mold under it, you may be able to brush it away with a small artist's brush, or blow it out using a can of compressed-gas duster available at computer or photographic stores. A light blast of Lysol, or something like it, might be helpful in arresting re-growth, as well as with the odor.
I'd tread carefully when cleaning the leather, which is very dark as you note. It may be that a prior owner "freshened" it at some time with a coat of...something, which darkened over time. If so, you'll need to determine what that something is. It might be shellac, which was commonly found in households years ago, and all too often applied to furniture to freshen the look. It may be a good idea, especially since you have an easily-portable loose piece of the leather, to consult with a rare-book restorer before you do anything much. The last thing you'd want to do is remove the paint. On the other hand, you may find that you get good results from a gentle cleaning with a product called Kotton Kleanser, or pumice free (that's important) GoJo. This kind of cleaning is probably a best bet before you do much else to the machine -- it will help you assess the overall condition.
If the machine actually was in a flood, as you suspect, and as it sure looks like, being sure that the horn is still tightly sealed will be especially crucial. One way to check this is to shine a bright light toward the front of the machine, while examining the horn assembly from the back. If you see light coming through, you'll need to seal those areas. Many collectors like to stabilize moisture in a dried-out horn by giving it a good soaking with a mixture of glycerin (from the drugstore) and denatured alcohol. Some say this doesn't make much of a difference, but I'm in the camp that believes it does.
The finish on the 8-30 was done with sprayed nitrocellulose lacquer, a departure from the previous use of shellac. It looks from your pictures that you still have a very restorable finish. It's quite possible that you'll be able to rescue it, after a good cleaning, with a product such as Howard's Restor-A-Finish. With any luck, even the stains on the top of the lid may be made tolerable this way.
For the missing piece of trim, if you have a decent picture framing shop in your area (one who makes their own mouldings), they should be able to help with that. If not, a good furniture-maker would.
Do you have the tone arm and all-important reproducer? They're not in your pictures, but you didn't mention that they're missing. The Orthophonic reproducers, as you may know, are much harder to work on than the previous kinds. If you do have yours, it may be made of pot-metal (which is likely for this machine), which is notoriously prone to degradation over time. Pot-metal reproducers may or may not be rebuildable, due to their tendency, if in really poor condition, to fall apart when disassembled. If you have it, can you post a picture of it? If you're really lucky, you may have an all-brass one, which was produced for a short time before Victor switched to pot-metal. The easiest way to tell is that a pot-metal version will have nine holes on the front, while a brass one will have only six (uhhh...seven?). If you do need to replace these parts, you'll be able to find them, but brass reproducers are always in high demand since they don't tend to degrade over time, and aren't cheap. There are a few reliable guys who do repair work for Orthophonic reproducers, and even a pot-metal one in rough shape can often be refurbished to a worthwhile degree though it might not be a candidate for a complete rebuild.
Congratulations on your find. It's an ambitious project, but I think that over time you'll end up with a real prize.
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) I wish I had the pictures of my dorm room, but unfortunately my iPhone was erased in the iOS 8 update! 
in the back of the machine, countless hickory nuts, and about 2 inches of dust in the area where the motor is. It also has a possible water line in the middle. I think it was involved in a flood. The feet are falling apart/missing. Veneer in many places is peeling, bubbled, very brittle. 
