Question: Why did it take so long for the Alien to burst out of the Predator? One burst out of Adele almost immediately upon her waking but it took about half an hour for it to happen to the Predator.
Answer: As mentioned in another correction, the aliens were genetically engineered for fast "hatching" and growth, with a human host. It is not unthinkable that the predator's different anatomy/biochemistry made it harder for the chestburster to develop inside it.
Question: Why were only three predators sent to deal with all the aliens?
Answer: As the film explains, it's part of a "rite of passage" ritual where a small group of chosen predators are sent to hunt xenomorphs to prove themselves worthy. The xenomorphs are the "ultimate prey" for them to hunt. There's only three because that creates more of a challenge for them to overcome. If there were more predators, it wouldn't be as much of a challenge, and thus it wouldn't really prove them to be "worthy."
Answer: The Aliens are trophies for the Predators, not some ancient mortal enemy. The 3 Predators are a literal hunting party sent for sport. This is why Danny Glover is not killed at the end of Predator 2 as he had managed to hunt and kill a Predator to its death.
Answer: Celtic is the second predator to die in the big fight. His death comes at the hands of "Nethead" (aka Grid) when he attempts to kill the alien with some sort of ceremonial knife while it was subdued with the net. He can be described as having an unusual mask because it displays some additional protrusions around the mouth, possibly as a re-breather of some sort. Celtic also has a scratch on his mask which he got when fighting the alien.