The tie-in book The World of Kong: A Natural History of Skull Island strongly implies that pterosaurs used to live on the island, but all except the flightless Scissor-Head went extinct. Why would this be? Because the other aerial niches on the island were claimed by the birds, "Vultursaurs," and giant flying rodents. By taking up wading and swimming after giving up flying, the Scissor-Head avoided competition with the rodents and birds, allowing it to survive.
It also helps explain why naturalists never knew that Skull Island was out there and so biologically unique until the Venture expedition. Had flying pterosaurs still been present on the island, they could've indeed flown to other habitable lands and been documented by science long ago. But Skull Island's endemic flying rodents can't possibly travel that far across the open ocean, mammals being far more dependent upon fresh water to drink than birds or reptiles. The seabirds on Skull Island aren't noticeably different from those found on other regional islands. The vultursaurs could have made it to some other landmass, but they're specialized jungle insectivores and would've had to compete with dozens of fish-eating birds if they tried to evolve to prey on marine life.
Unlike the 1933 film, Kong fights three Vastatosaurus rexes instead of one Tyrannosaurus rex. Though it may look like a contrived coincidence to make the fight look even more remarkable, there is some brilliance to this. The World of Kong: A Natural History of Skull Island says that Skull Island has been sinking into the sea for the past thousand years. As the V-rex's natural habitats dwindled, they were forced to share their hunting grounds with other V-rexes and predators. From these standards, it wouldn't have been realistic for Kong to fight one V-rex and not expect at least another to stumble across them.
Why does Kong climb the Empire State Building? His lair on Skull Island is the island's highest point; Kong could see the entire island from there, and most island predators couldn't reach it. The place signifies sanctuary for Kong, so he likely got the same feeling upon seeing the Empire State Building—the city's tallest building. Kong believes he is taking Ann somewhere safe.
The 1976 film used the same concept, with Kong likening the Twin Towers to his lair.
Why are the Vastatosaurs so fixated on killing Ann when they have better options for food? As V. rex is a tyrannosaurid, it likely has a strong sense of smell, and Kong's scent is all over Ann. As this is the first time a human has survived Kong, they likely thought Ann was an infant of Kong's species. As Kong is their biggest threat, they're desperate to kill Ann to stop her from becoming a later rival.
Why is Kong initially violent to Ann, why does he handle her roughly after taking her, and what explains Kong killing his past sacrifices? Since becoming the Last of His Kind, Kong had to live a harsh and lonely existence with countless hostile creatures fighting him for dominance. With no more family, Kong also had no means for meaningful interaction with other animals on his mental level. He also had to endure the routine of the natives offering him a sacrifice, of which Kong would quickly become bored, making him work himself up into a rage to kill them. This may have made Kong somewhat feral. There is truth in Real Life about Kong becoming aggressive due to a lack of other sentient beings with whom to socialize. Like humans, gorillas are naturally social animals, so one regressing to their innermost primal instincts and showing behavior atypical of their species from intense isolation isn't unusual.
Kong would've killed Ann like the others, but she changes his routine by fighting back, running from him, and having people come after her. Ann later entertains him with her vaudeville skills, piquing Kong's curiosity and allowing him to form an emotional bond with another being. This saves Ann's life and may explain why Kong grows so attached to her.
Besides grieving Kong's death, what else is going through Ann's head after he falls from the Empire State Building? According to the film's audio commentary and novelization, Ann considers suicide; she's so close to giving up after watching Kong die that she almost wants to follow him, but Jack's arrival pulls her back from the edge.
One for the video game. An unlockable secret ending has Kong survive the film's events and return to Skull Island. All fine and good, then you remember that according to tie-in materials, Skull Island is slowly sinking into the ocean, and everything on it is doomed anyway. Poor Kong can't win.
