How do I save these chairs? Actually, what is this set?  

Obviously, I don't know how to post photos
But the link to the Flickr page works, if you are interested.

Shoot!
Karlit is an international company that makes MDF. Maybe they made just the MDF used to make the china cabinet.

Nice !
I suspect the rusting steel is not a serious structural issue. The wood is no doubt glued to the steel in a way that would prevent removal -- unless you see screws through the metal into the wood ? I wouldn't worry about it; medium steel wool to remove excess corrosion, and oil or wax to inhibit further rusting. Anybody have other advice ?
Original upholstery in good repairable shape is worth more, aesthetically and value-wise, than new, I think. It's a pretty set. Can we see inside the cabinet ?
Love it !

Yay!
Apparently there's a lag when posting pictures, but I'm glad they are here now.
Thanks, SDR. I like it, too. When I saw it, I called immediately. I wasn't too sure about an all formica china cabinet, but it looks pretty good in my room.
About the chairs: The wood was stapled over the steel. The base pictured is in pretty good shape, but some others are worse. I think they are all structurally sound, but unfortunately, I can't use them until they are fixed. They are missing most of the plastic slides, and they will rip up my floor.
I know original upholstery is always best, but clean and fresh has it's benefits. 🙂 They are in fair condition, but I've got a lot of cleaning ahead of me -- especially at the edges. It looks cleaner in the picture than it actually is.
I'll add the inside pictures soon.
Thanks again!

More picutes
We've finally had a bright, sunny day, so I have posted some pictures of the inside of the cabinet. It's mainly painted mdf. It has a silverware drawer.
Photos are on Flickr, along with some other new and better shots. Thanks!
http://www.flickr.com/photos/37542328@N06/sets/72157622708888678/

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Thanks for the photos. The wood caps on the chairs are stapled to the metal ? I've never seen this. Where are the staples, and how do they penetrate the metal ? If they are only stapled, the staples might be partially removed from the inside, assuming the metal feet are hollow and open at the bottom. Thin metal like staples and pneumatically-driven nails can be broken off at the surface of the material they protrude from, by gripping them with snips or needle-nose pliers and wiggling until the metal fails. If the staples are thus terminated, perhaps the wood caps can then be urged off. If this leaves the staple remains soundly covered by existing wood filler, the last remnants could be carefully snipped off on the inside and left alone through any refinishing procedures. Alternatively, the staples could be removed entirely from the wood, after which filler could be applied to the damage prior to refinishing.
I would have expected the caps to be glued on, perhaps with a hot-melt that might be reactivated with steady and patient application of a heat gut (hair dryer). Scorching would indicate too much heat. I presume you'd plan on refinishing the wood while it was removed from the chairs. The metal could be sanded with medium and fine papers to remove the rust, and an application of fresh paint, followed by reassembly with an adhesive to be determined.
The pieces do look nice. I question whether the table and chairs were originally parts of a set, because of the different forms of the feet and color of wood/finish, between the two -- they could have been purchased at the same time by the original owner, of course. They are all quite cool -- especially the table base, which I feel I've seen before. The "veneer" inside the upper cabinet is revealed to be a printed foil, by the (too) perfect repeat of the grain pattern. This would be quite common for MDF-based case goods. The special qualities of the piece are all evident on the outside. . .

Thanks for looking!
I appreciate your input, SDR.
I was wrong about the staples. I think someone fixed one with staples, and that's what I saw. You are right -- they were likely glued.
Upon looking closely at the bases, it's a poor design. The problem is, the wooden covers do more than hide the metal -- they hold the plastic slides, which were tacked in. So weight in the chair is constantly pushing the wooden covers up and pushing rough metal pieces down. The plastic slides have to placed exactly over the metal with hope that they won't shift -- not a good way to protect a floor. I'd say that the plastic slide, then the glue, then the metal base are holding up the chair. I hope that makes sense, and is it any wonder the bases are coming off?
I question whether the whole set was original, too. To me, the chair bases don't match, with the routered detail. Certainly, they've been together for a long time, but there are extra holes on the chair bottoms -- maybe the bases were switched out.
BTW, here's a fun fact. The woman I got this from bought it in the '60s from a woman who was redecorating to all antiques (my seller still was aghast all these years later). And my seller reluctantly sold this to make way for her late mother-in-law's Herman Miller dining set. 🙂

Ha !
Interesting stuff. Yes, you explained the chair foot situation very well -- wish everyone could do that well. Odd, isn't it -- not a good arrangement at all. Assuming you could get the wood caps off, they could be epoxied on and probably carry any amount of weight. But an elongated metal/plastic glide that picked up the end of the metal would be ideal, I guess.
I'm wondering how the dog-leg bend of the table base is structured. Metal hidden in or below the wood ? I can imagine a substantial wood spline. There's a lot of stress on that joint. . .

Looks like it's all wood
I posted a picture of the bottom in the gallery for you, but I don't see any metal joinery. One of the legs has a tight but long crack, and a couple of the joints at the bend have slight separation. Maybe the previous owners were careful with it, or maybe the fact that there are six legs distributes the weight enough to spare it. The table top isn't too heavy and if they have good manners, elbows would be off the table. 🙂