There's a common trope of the female sex worker in the wild west (complete with what she might've looked like, where she might've worked out of, etc.). I want to use this as a jumping-off point for male sex workers in that time/place:
I did try a quick google search, and most results are simply people asking the question without a lot of answers. This article is quite interesting but talks about homosexuality rather than sex work.
NOTE: this is a repost of my previous question at the direction of a mod, where I used the word 'prostitute' rather than 'sex worker'. thanks for the feedback! a lesson learned for me, and a great reminder about being careful about language.
This is one of those questions that is impossible to answer adequately. I have never seen nineteenth-century evidence of a professional male sex worker. But the fact that I haven't seen the evidence doesn't mean that there is no evidence. The West is the largest region of North America and among all the expanse and all the decades that are perceived as belonging to the "Wild West," anything is possible.
It is entirely possible that there were some private transactions: there were probably examples of a woman or a man giving money to a man with whom she/he had a sexual relationship. That did not make these men sex workers in the sense of an occupation involving sexual commerce with multiple partners. Those men would not be known in the community as sex workers, rendering all your separate questions inapplicable.
If I could find a man who was a sex worker in the nineteenth-century West, I would have written a book about him. I wish documentation existed, but I have not encountered it.