That is a very special grill made by the original PK (Portable Kitchens) company. They have a cult following of sorts - even a small FaceBook group. It is about the diameter of a Smokey Joe but tall enough to do more. With two bottom vents and the original flip-up grate you can even do a low and slow bbq pork butt. It will, of course, also do high heat grilling.
The missing bottom vents can be obtained from Johnny Joseph on the PK Fanatics group on FaceBook. He makes stainless replacements. I used a pair of his on my Duchess. As far as the burn-through, that is likely the result of a prior user just dumping charcoal in the bottom after the original cast iron charcoal grate was no longer useable. I wonder if you could make a patch with JB Weld Ultra High Heat. You may have to replace the patches now and then.
These are cool historic grills. Unfortunately, the "new" PK company has not decided to bring the Duchess back and does not support them. It looks like the seller has already gotten parts you need other than the bottom vents.
In spite of the minor damage, I agree with Mike-LA that it is well worth the asking price if you like cool, old grills. Also, the cast aluminum does radiate heat well, so they are, in fact, good little cookers!
Here are a few pictures of mine, including one of the replacement vents:
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