Yes, they do. See the related link for further information.
I have never heard of the Atacama Desert Islands. Are you sure you know what you are asking? I have heard of the Atacama Desert in Chile, Peru, Bolivia and Argentina but not the Atacama Islands.
No.
No one lives on a desert island. That is why they are called desert islands.
Forests exists on mountain ranges that are like islands in the desert. However, they are not part of the desert and are separate biomes. The mountains receive a bit more rainfall and snow that the surrounding desert and are able to support more vegetation.
in mexico
No
The islands were formed from erupting volcanoes.
Lanzarote, one of the Canary Islands, is considered to have a desert climate.
Aquatic and marsh animals do not exist in deserts .
El Capitan is a peak in the Guadalupe Mountains which are located in the Chihuahuan Desert. The mountains themselves are not part of the desert but are islands in the desert.
The Orange Islands do not exist in any Pokemon game.
because if they weren't there, there wouldn't be anything for the big islands to tease.