Learn English – Differences between ‘plead’ and ‘beg’

A scream is always loud and may or may not be sudden.

They screamed in terror.

If a scream is high in pitch it turns into a shriek.
A shriek is always loud, high in pitch, and is usually sudden.

She shrieked in horror.

Shrill is high in pitch.

She had a high, shrill sounding voice.

Women's voices, not men's, are more usually characterised using shrill or shriek.
Both men and women scream.

shriek = scream + shrill

X is necessary for Y

This expresses a prerequisite. Here, you are saying that if you don't have Y, you can't have X.

X is necessary to Y

This can be interpreted as "Y believes X is necessary", but this may not match what you think is necessary or what actually is necessary.

In the case of life, air is objectively necessary (for some life anyway), so you can say to or for.