Bows and arrows vs. plasma casters and wrist-mounted nukes? I assume that's a rhetorical question? The predator has the navi totally outclassed in terms of strength, speed, endurance, durability, training, stealth, firepower, and senses. The only thing they are remotely similar on height and climbing ability. I doubt a navi even caries enough weapons to kill a predator, their arrows are lethal to humans but would probably be an annoyance at best against a predator since the predator is likely too fast for the navi to get a clean hit. And that is assuming we are only dealing with one predator with standard-issue fear. If you let the predator have some of the more powerful gear you see in the comics or some of the big guns you see in the AvP movies then it would be even less of a contest. The weapons-matching rules the predators use is not really an issue, the predator in the first movie had no problem using his shoulder cannon against a bow and I imagine the dart gun and net gun would be treated similarly. Their spears, axes, nagitanas, swords, and other bladed weapons would all be fair game. And even if by some miracle the navi won, he or she wouldn't have enough experience with technology to realize what the wrist nuke is until it's too late.
As for navi vs. aliens, that depends on how many there are. One-on-one, if the navi new the alien was there and got really lucky it might have a chance if there wasn't any deep water and it was daytime (if there was deep water and/or it was night then the navi wouldn't stand a chance). If it didn't know the alien was there, the navi would be dead before it even knew there was a fight. But multiple navi against the same number aliens would be a rout, the aliens would attack randomly from all directions, throwing the navi into confusion and picking them off. Even if a navi managed to kill an alien chances are its blood would take out one or more of the other navi, and aliens take even more damage to kill than a predator. This is assuming we are dealing with aliens from human hosts, if the hosts were navi then that tips the odds even more in the aliens' favor.