You are correct, and there is certainly a lot of fake rocks and painted cement in this all-indoor exhibit. Although it is interesting to see sway poles for the primates, as usually zoos resort to hanging ropes for monkeys.
Depends on whether 'tropical' is meant geographically or climatically. A Tropical Climate is generally humid, so won't be a desert, but 'tropical' geographically just means between the Tropics of Cancer and Capricorn, so several deserts/semideserts are at least partially tropical.