They're around; at least 10 holders in NA, 5 in Europe, as well as Jurong. Also relatively rare but present in the private trade.
Other than DWA, they are also at San Antonio Zoo and Santa Fe Teaching Zoo, Dallas Zoo and Zoo Miami did have them but I don't know if they still due as I didn't see them on my last visits.
I’ve seen a single bird at a pet store a few years back. I think they are territorial and demanding, and aren’t commonly kept for this reason
In South Africa, Hawk-headed Parrots are kept at Exotic Animal World as well as present in the private trade among more daring bird keepers.
According to Zootierliste, ca. 20 zoos keep one or more subspecies of Hawk-headed Parrots in Europe (including Russia). 2 of them are in France (Upie and Beauval). It isn't common but not extremely rare in European zoos and bird parks.
Are bohor (or any other) reedbucks kept in captivity? I saw some of these this summer in the wild. They are pretty neat.
Sharjah Safari park in the UAE imported some from South Africa in 2017. These were southern reedbucks (Redunca arundinum). Tierpark Berlin in Germany & Dvůr Králové in the Czech Republic both hold mountain reedbucks (Redunca fulvorufula fulvorufula).
For a question like this, I'd suggest using Zootierliste. Using the search feature, you can find info on a bunch of captive animals and where they are held (though it is mostly restricted to European zoos/aquariums). Anyway, to answer you question about the brown hyenas, they are held at two institutions: ZootierlisteHomepage
There's 20 current holders according to the most recent studbook in North America, so while they're out there, they're not common by any means.
Are there any Lord Howe stick insects on public view in mainland Europe? Any closer information where those mythical Galapagos iguanas are supposedly kept privately in Switzerland?
These animals are in private hands. They belong to T. Price, the owner of the CTC Conservation Center in Uganda. His collection in Europe is definitely not meant for visiting. You might be able to arrange a meeting with him in Uganda. But since it is likely far away for you, why not focus on seeing these majestic species in the wild? That is, in the end, always the most beautiful place of all.
I thought that all Galapagos iguanas (land and marine, if any) moved to Uganda years ago. Another animal in Switzerland I wanted to ask is Spix macaw. I suppose it may be an urban legend, because it was never located by anyone including Swiss police. I suspect it died from old age decades ago, possibly before the rumors started.