We don't actually see any animals dying. However, two giant birds fly into each other at full speed, which may be fatal for one or both of them. Also, another giant bird is caught in a spider's web, and we see the spider crawling towards it, which most likely spells its doom.
when they're being chased by birds, they briefly fly past a spider (54 min), and the last chase ends with a bird being caught in a web and you can see the spider in the background approaching it (56:55 maybe).
at 1:13:00 they're at a web with a spider in it, but they don't interact
Michael Caine's character makes a joke about his own weight: "I've never been able to crawl through that tunnel. Too many fried eggs, I'm afraid" (touches his belly and laughs).
Well, a helicopter. We see the pilot losing control and the chopper losing parts when it's sucked into a twister. We don't see it hit the ground; there's a black screen, after which we see the characters on a beach, unharmed, the chopper having plunged into the sea.
No, but all of the main characters are in imminent danger of drowning - Caine's, Guzmán's and Hudgens' especially dramatically so, since they don't have any means of rescue in sight and are surrounded by falling rocks.