Yes, the businessmen who hired Chigurh also hired other hitmen to track Moss down. Chigurh finds this insulting and infuriating and it's one of the reasons he goes back and kills the businessman in the high rise (the other reason was because that guy had hired Wells to kill Chigurh). But to answer your question directly: Yes, the Mexicans who were in the hotel in Del Rio also had a receiver.
As to why Moss didn't get rid of the tracker when he found it, no answer is given. After he found it, the book says Moss realized he would probably never be safe again in his life, so Moss was probably thinking he would just wait for Chigurh and kill him. (Remember that Moss had asked the clerk to call him if anyone checked in, so that's why he felt safe enough to lie down). Later on in the book there's a passage in which Chigurh says, "The prospect of outsized profits leads people to exaggerate their own capabilities. In their minds. They pretend to themselves that they are in control of events where perhaps they are not." So it's safe to say Moss didn't realize what / who he was up against. Yes, he was a badass in his own right, but he wasn't badass enough. He exaggerated his own capabilities and he underestimated his enemies.
In the end, the Mexicans found Moss by tapping the phone of either Sheriff Bell or Carla Jean Moss. Carla Jean told sheriff Bell where Llewellyn was. All the hitmen knew Moss was traveling along the border and that he was trying to get back to his wife. The towns are small and populations sparse along the border (even more so back in 1980) so there weren't many places he could have stayed along the way without being found. (Remember that the Mexican hitman actually killed Llewellyn. Chigurh arrived at the motel afterwards and retrieved the money - which no one else had found) Sometime after Moss was killed and Carla Jean's mother died, Chigurh went to Carla Jean's mother's house (which would've been easy for him to find) and killed her.