AIt's a different Predator. The Predator in the first movie blew himself up with a (possibly nuclear, but more likely some sort of electronically charged blast) explosive that, according to Keyes, took out the equivalent of 300 city blocks. The Predator in this movie is also different in appearance. The names of the two Predators are Jungle Hunter (Dutch's Predator) and City Hunter (Harrigan's Predator).
AThe Predator's reasons for skinning his victims and hanging them is not explained in this movie nor in the first movie. It was established in Predator that the Predator is a "hunter", and hunters will often gut and dress their prey while still in the field. Game animals are also sometimes left hanging for days or weeks in order to season the meat before consuming it. However, the Predator in this movie goes to an abbatoir (slaughterhouse) to feed on beef, so it's unlikely that it is also feeding on humans. It was also established in Predator that the Predator removes body parts, e.g., skulls, spines, and hearts, as trophies. Another theory that's been suggested is that the skinned bodies were deliberately left hanging as a warning to other humans in the area, either taunting them or letting them know that they are also being hunted. In other words, the Predator is taunting its prey, as it is stated in the movie, "to scare the shit out of its enemies" like the Jamaicans do. Another possibility that has been suggested is that the skinning and hanging of their victims is a religious or hunting ritual. Some human cultures have the tradition of marking a novice hunter with the blood of his or her first kill. Skinning the victim could signify that the prey is rendered "naked" and defenseless. Hanging the prey upside down may, according to a Predator, prevent the spirit from ascending, trapping it inside the body, making the kill more valuable. Another theory is that the Predator may do this to victims it finds unworthy to become "trophies". Harrigan, King Willy and Jerry all put up a significant fight against their foes and also stand their ground against the Predator when faced one-on-one, whereas a whole group of Colombians and Jamaicans panicked and were dispatched very easily. Notice that it wasn't mentioned that Danny was decapitated either, so given the way he panicked and begged before he was killed and his fight only lasted all of 10 seconds, the Predator felt he was not trophy-worthy.
ANo, they can be killed and obviously have a high mortality rate given the nature of their culture. However, it may be inferred they age slowly and have an extended lifespan. The Elder Predator that gives Harrigan the pistol was clearly frail. The pistol dates 1715 which may suggest that Predator survived his "trial" and claimed that as his trophy during his "coming-of-age" ritual. If that is true then it could be surmised they have a lifespan of around 300-400 years. There is also the possibilitythat the apparent long lifespan is due to time-dilation from space travel. It is part of the theory of relativity, and it has been proven that traveling at fast speeds causes time to slow down for the person traveling. If we assume that the Predators' space travel includes getting to very high speeds, visits to Earth every hundred years might only be a few months apart from the Predators' point of view, meaning they have no different a lifespan than we do.