I don't think so.
the Joshua tree
Nevada
No
As a young boy Manson lived with his grandmother in Morehead, located in Rowan County, Kentucky
The Joshua tree gets eaten by many animals. When a tree is just sprouting, a deer or rabbit might eat from it. Parts of the tree can even be cooked and eaten by humans, although, some parks laws prohibit this.
I doubt Charles ever stayed there. I could find nothing to confirm that he was ever there.
There is no such thing as a "Joshua Cactus." There is, however, the Joshua tree which is a tree-like yucca found mainly in the Mojave Desert. It can live for hundreds of years and some specimens as old as 1000 years have been found.
The Joshua tree is only located in the hot areas of North America, such as California, Arizona, Utah, Nevada, ect.
I could find no evidence that Manson ever lived in New Mexico. ~ Charles Manson was convicted on Mann's Law for transporting a woman from California to New Mexico for purposes of prostitution. As to whether it was Lordsburg or not, I don't know yet.
spahn ranch and barker ranch
Yes, the bobcat does live there. The bobcat is a species of lynx.
Although it appears that Manson himself did not live in Woodbury but he does have ties to that area. Manson's mother Kathleen Madox settled in the Short Mountain area of Cannon County, TN., after Charles was an adult. He did live in Grahn, TN, with his mother at his grandmother's home. Rumors of a devil-worshipping cult active in the hollows of Cannon County that have been linked to Manson and the Family have swirled for decades but very hard to substantiate. It is now common knowlege that Manson was involved in devil worship starting as far back as the 'Summer of Love' in San Francisco in the 1960's. Manson had dealings with Anton Le Vey, renowned satanist, and the cult known as the Process, as did Susan Atkins, a Manson diciple.