That unit has reached the end of its life, I'm afraid, and should be replaced. Better to do it now, while it's still "exposed", and before you go to the expense and trouble of adding a chimney cap and facing material, than prolong the inevitable. As for determining the manufacturer, there should be some sort of metal identification placard on it, perhaps behind the hood. If there is it's likely covered in soot, which is making it hard to find. But even if you are able to determine make and model, I highly doubt you'd be able to buy replacement parts and/or accessories, OEM or aftermarket; it's just too old.

Wow, if this were my place I would rip that old unit out and replace it with a modern air tight fireplace unit. That unit is a prefab and it looks like it has seen better days as it's 30 years old. A nice modern EPA rated air tight fireplace will save wood and burn cleaner as open fireplaces literally suck the heat out of the home and puts it right up the chimney creating a "negative efficiency". The only place you're warm is right in front of the fire. An air tight unit will generate heat and as someone who uses a wood stove for my primary heat source I'll say you can't beat the heat from a wood fire. Here are some examples of excellent replacements:

When you measure, add at least 10% to the amount to account for things like irregular cuts, pattern matching, mistakes, later repairs and so forth. I would actually go a bit more -- when I did my FR with the 10% extra tiles, I ended up with only 2.5 tiles and some smaller scraps left over! Brands -- I think that Supreme Elite, Mannington Adura, Congoleum, IVC, Shaw, Mohawk, Armstrong are all well respected names -- I am sure there are more that I don't know. But all manufacturers make different grades of flooring, so you kind of need to know what you want. In general, I believe for vinyl, the thicker the core layer, the better, especially if you are doing a loose lay or floating installation (not glued down); same for the wear layer. Thicker is more expensive - get the best you can afford! But IIRC if you are doing glued down sheet vinyl, that won't be as thick. Start visiting the websites of flooring retailers so you can get an idea of what is out there. Also the retailer that I mentioned above has helpful information on their website -- I expect others do also. There is a flooring forum here on gardenweb too, a good place to ask questions. Also go to some flooring retailers so you can get a feel for the different grades/types of products, how they look and how they will perform.

Jennifer - I'm not a pro, so I really cannot offer any advice. Just want to let you know that I really feel for you. I'm in the Chicago area and I wish there was a way I can direct message you as we had our basement finished last fall and was happy with our contractor. We also got new countertops last year and was very happy with our fabricator. I hope neither was the company that you worked with. I just want to correct you in that Cambria is not the only company whose quartz does not come from China. There are many others. The "cheap Chinese" quartz that a lot of people talk about on this forum are companies that do not use the Brenton technology. I will say though that I agree with you on your assessment with how a lot of the Pros "talk" to the homeowners on this site. It can certainly be frustrating. I don't know of a "designer" around that will work with a small project -- and the first thing the Pros will tell you to do is consult a designer. Great - tell me one that will work with a budget that less than 100K. Or a small project as many of us don't have the financial resources to do a giant project at once. It sounds like you did your research and I'm not sure if there is a problem with the fireplace not being a vented fireplace that caused the issue but if Quartz Masters said it was fine, then I would "think" they're at fault.