Star Trek

Well, we gotta establish a couple things to start with.

A. Gorn Eggs: How many are born from a cluster? We see 4 burst from Buckley in the episode so I'm going to act on the assumption that 4 is the usual number. They're also hostile to each other immediately upon birth.

B. Gestation Period: In humans its hours, in Orions its weeks, but Buckley is a completely unknown alien species. No clue how long the gestation period actually is. As you stated though, it doesn't really matter when Buckley was infected due to the variation.

C. Civilians: The Civilian Passengers were Oriana, Buckley and Pasko. Everyone else on board was Starfleet personnel.

D. Sensors: Gorn, and their eggs, are completely invisible to them at this point. Biofilters can't even grab the eggs.

With those established, it becomes a bit easier to answer the remainder of the questions.

1. The bodies are just outside and hard to find. Over the course of a week, Starfleet officers died trying to kill the Gorn We don't know exactly how many but it's somewhere around 80. They found 20 crewmen outside but M'Benga says that there could be more bodies that they didn't see. We know they didn't do an extremely thorough search of the area because of the elements and the hike to the ship. Gorn bodies also wouldn't show up on the tricorder and their numbers would have been far fewer, maxing out at 4. The search area and limited search tools mean they would have had a lot of difficulty locating Gorn corpses under the snow.

2. Pretty much. Over the course of a week they probably killed one gorn. Likely through some sort of coolant leak or something that showed they were cold blooded. The rest of the crew made the plan to lure the Gorn outside and freeze it to death. They succeeded but they also lost their way back to the ship and were stranded. We didn't see any other Pasko-Gorn on the Peregrine and Oriana is still alive so it's safe to assume that the Peregrine Crew succeeded in killing Pasko-Gorn.

3. Pasko blew himself up with a plasma grenade inside of main engineering. It wasn't an enormous attack on the ship itself so much as a pressure point that got pressed. The matter-antimatter reactor was 'busted' according to Uhura and it damaged backup batteries. Without that the ship had extremely little power. They re-routed what little they had from the warp core injectors as emergency power. So the ship was damaged but in a survivable way. Hell, it even survived the landing on the planet. We see from the shots inside of Main Engineering that it had very little physical damage that could be ascribed to an explosion. We don't know much about Plasma Grenades but my assumption is that it generates plasma and throws it in all directions instead of simple shrapnel. If so then it wouldn't destroy the body like a typical explosion. It might shred it and do extreme damage, but major chunks would be overall 'intact'. The Gorn hatchlings are also pretty small overall as well as durable so I can see them surviving it not just from toughness but also because the chances of the grenade shredding the Gorn inside of the host body was pretty small.

Conclusion: Pasko successfully disrupted ship operations to the point it was forced to make an emergency landing, however he was unsuccessful in providing a large enough explosion to destroy the hatchlings inside of his body. The Peregrine crew led the Gorn outside, successfully, but died in the process themselves. The Gorn bodies were left somewhere in the field near the ship but remained undiscovered by the Enterprise crew due to (a) sensor limitations, (b) size of search area, and (c) time constraints imposed on them, especially when recalled by Pike.

Those be my thoughts at any rate. Not sure if that'll help you with your own conclusion but I hope it does.

We have to accept that Gorn biology has no tolerance at all for subfreezing temperatures. The Gorn young are functioning at an instinctual level, they would learn by lethal experience. Unlike the adult Gorn in 2 x 10, they would not have the protection of environmental suits.

As I would very much love for Hemmer to be somehow still alive, having survived the fall and a period of low temperature semi-hibernation, anything that brings Starfleet back for follow up would be welcome.

I’m going with assumption that the plan to lure the more developed Gorn outside was successful, but could not address any new ‘infections’ in survivors. Hemmer repeated the plan, but as an Aenar, evolved for extreme subzero temperatures, and more physically robust than a human, there’s no reason to believe he died, no matter that he was willing to sacrifice himself for his shipmates. (I’m willing to go with his using his abilities and some kind of sharp tool to stop his fall and find a crevice to hibernate in.)