Nope, South America is the epicenter of diversity in cacti. (A ton grow on trees or rocks in semi-jungle areas.) Mexico has a ton too, the US has relatively few native species compared to anywhere in the Americas. *Cactus are only native to North and South America, anywhere else around the world they've either been planted or escaped cultivation. One species is through to have been carried via birds from Brazil to West Africa. (Rhipsalis baccifera I think?)
No, they are in deserts all around the world
Thanks! Your answer is awaiting moderation.