Can I use it and its for people?
The fear is the essential attribute of a human nature. It figures a crucial role in its survival.
where its means human's.
Can I use it and its for animals?
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This is probably better:
Fear is an essential attribute of human nature. It plays a crucial role in their survival.
It is not generally considered appropriate for humans. We use he, she, etc. It implies that the human in question is an object, or has no gender (which is generally considered offensive).
As far as animals go, it and its are fine.
The beaver, commonly known for its ability to cut down trees, is known as a national symbol of Canada. It was regarded as valuable (for its hide) many years ago.
You can't use "it" for humans. I'm a little confused by your example, but I would say:
Fear is the essential attribute of human nature, and plays a crucial role in human survival.
I took out the pronoun because using any sort of pronoun in "__ survival" seems odd here, because we don't readily parse the word "human" as its antecedent since it's part of the phrase "human nature", which gets interpreted as one word. A version with the pronoun might read like:
Fear is the essential attribute of humans, and plays a crucial role in their survival.
As for animals, you almost always use "it", unless you're talking about a specific animal that has been personified/humanized in some way, or that the speaker has an emotional attachment to (usually a pet). For instance, after meeting your friend's (female) cat, it might seem rude to say "Its fur is pretty" rather than "Her fur is pretty".
'It' can be used for someone whose sex is not known. You can use it for a new born baby. E.g. It is a baby. Also, you can use 'it' for one who is knocking at the door, especially if you do not know the gender, e.g. Who is it.
Futhermore, you can use 'it' in an offensive way for someone whose gender is known but for the purpose of belittling him or her.