1. He (might be a security guard) cried, "Stay back",
and a monster(looks like a hyena) killed the security guard.
The monster's fellow said, "He should've said "heel""
This is a joke [ and a bad one :) ] in reference to the monster that resembles a hyena. Hyenas look a lot like dogs, and "heel" is the common English command that we use to tell our dog to follow us. The heel is the back part of the foot, so telling a dog to "heel" is telling him to follow you at your heels. It's a really bad joke! I think the speaker is referring to how the security guard said, "Stay back!" He seems to be implying that the guard should've said "Heel!" instead of "Stay Back!" because the monster looks like a dog. It's a terrible joke because it really doesn't make sense. The two declarations don't mean the same thing at all so the joke falls flat, as we say. Sometimes cartoons have really terrible jokes.
3. The monster crashed again, so dancing girl? said, "Delicate like a moose"
She just used an irony?
Using "delicate" in this circumstance means something similar to "careful" or "precise". The monster has crashed more than once, so the girl is making a sarcastic remark. She's saying, "You're as careful as a moose." A moose is very large and doesn't pay any attention to all the things it steps on or knocks over while it walks through the forest. So a moose not careful at all! I'm not sure if irony is exactly the right term, but it's definitely sarcasm.