You should really consider seeing them in the wild (or what remains of it) one day (post COVID-19). You can see them very easily at Poco das Antas biological reserve in Rio Da Janiero state. The reserve is run by one of the best long running conservation NGO's in Brazil "Associação Mico-Leão-Dourado" which is a very impressive organization (the other most successful conservation NGO in the country "IPE" incidentally also focuses on a tamarin, the black lion tamarin, and is also brilliant).
Very easy question! It's the monkey species that I saw most recently, so it changes regularly. At the moment it will be the black and gold howler, as they are the species nearest the exit of Paignton, the last zoo I visited before lockdown.
Last monkey(s) I saw was the de Brazzas at Twycross just before I left the zoo, but they are a favourite anyway.
Man, that is a tough one... If I had to choose, as far as extant taxa are concerned, I would say langurs or members of the genus Macaca. For extinct/fossil taxa, I would say the genus Paraloutta because of their obscurity and distribution range. On both counts, there are no native primates living in the Caribbean today. Paraloutta was native to Cuba and was likely an example of island gigantism. You can read more about this genus here; Paralouatta - Wikipedia
To be honest, I've never been particularly interested in monkeys, as apes and lemurs have usually been what's caught my interest. Lately though (largely due to ZooChat folks ) I've been introduced to a lot of primate species that I previously passed over, and it turns out I really dig Old World monkeys as well. Several langur and macaque species (Javan langurs and lion-tailed macaques are some standouts), as well as hamadryas baboons and mandrills, are animals I'd love to see with fresh eyes.