EVERY

It is used before a singular noun, and needs a singular verb

Every day is different (not: every days are different)
Every child was sleeping

negative:
Not every child was sleeping, two of them were talking

But if we use a pronoun or possessive with EVERY, we normally use it in the plural (especially when talking about people)

Every student took their book and went away (...took his/her book... is very formal)
I can't phone every person in town to tell them the news
Suddenly, every child woke up and they all started to cry

The same is true for compounds with EVERY: everybody, everyone, everything, everywhere

Everybody is free to do it or not
I talked to everyone to convince them that they should help
Everything was clear to me
I looked for my dog everywhere, but couldn't find him

EVERY vs ALL

The meaning is basically the same, but they use different structures
 
Every is = All are
Every child needs love = All children need love
Every light was out = All the lights were out
 
We don't use EVERY in front of articles, possessives or demonstratives, or with uncountable nouns
- All the birds flew away (not: every the birds)
- I've written to all my friends (not: to every my friends)
- All those people were looking for a restaurant (not: every those people)
- I like all music (not: every music)

EVERY vs BOTH

If we only talk about two people or things, we use BOTH

- I have three sons. They all have a car
- I have two sons. They both have a car
- We both need a break
As a subject, BOTH goes in "mid-position" (before normal verbs, after special verbs: modals and auxiliaries)
- we're both Spanish
- we both work here