A couple of questions

Actually I am pretty sure it was slowly dying from the shotgun wound. Which is why it tried to blow itself and Hardigan up.

Also, I'm pretty sure if they wanted him to go with them, they would have forced him to go with them. Also part of the premise of Predators was that the people who were sent to the planet had never fought a predator. Hardigan going would upset the Predator's intentions as he'd be able to help the other people there fight the predators.

They’re not the smartest aliens in cinema - they’re sport hunters who don’t mind blowing themselves up to protect their tech (“Predator”) or ensure an honorable kill (this film).

I thins the predator says it best, “shit happens.” It wouldn’t be honorable to risk falling and dying with his prey still alive, so he may as well go nuclear.

That’s my theory at least.

As for the “take it” predator, it seemed like they’d assume he’d leave but maybe didn’t care much one way or another. At least one novel and comic tie-in has a human (“Yoo-mon”) join a predator tribe and go hunting off world.

I think they stole that plot point from the “Critters” films where a bumbling human winds up joining a couple of alien bounty hunters

And one version of “Predators” was going to end with Schwarzenegger himself as Dutch showing up in a predator ship to rescue the last two survivors, laying groundwork for a sequel and implying that humans and predators are cooperating to some extent.

1. city hunter aka pussy face was sore loser bitch and wanted to take harrigan with him. he was not dying but would die without treatments. when harrigan chopped off pred's hand he treated himself and was ok to run back to mothership. but he was not dying he just was sore loser and was disappointed his hunt was failing.

2. if harrigan had stayed on ship they probably would have kill him

The fall would kill the predator, so he activated the bomb.
He still falls but is saved by grabbing the pipe randomly.

It was hurt badly would it have died or not it really doesn't matter but remember these are warriors it had been defeated.

In the first film it was the same sort of thing.

Him being given the gun was a sign of respect it's a trophy this is how they are it's about trophies.

He wouldn't be put out for hunting he had proven himself to them by beating one of them if anything they may have accepted him into the group.