The most common would be the locusts and grasshoppers.
Desert lizards eat bugs that live in the desert.
There are many, many animals that eat plants and live in the desert. However, there are no deserts that eat plants.
By definition, in the desert
Yes, plants live in all but the most exteme of deserts such as the Antarctic where few plants live and are rare in the Atacama Desert.
An ecosystem is a place where plants and animals ( maybe humans ) live and animals and plants live in the desert so … 
Some of the plants that live in the Simpson Desert: Canegrass Acacia Parrot Bush Spinifex Grass
Parasites.
You would probably have to eat bugs and snakes and maybe animals.
Armadillo lizard, Desert tortoise, camel, desert rat are the only animals that live in the desert.cactus, Soaptree Yucca, Mojave Aster are the only plants to live in the desert
Xerophytic plants live in the desert scrub.
Aphids can be found in any warm or hot desert which has plants upon which they feed.
Biomes.