"Everybody hold hands" is a command. Your are commanding them to hold hands. "Everybody holds hands" is the present tense of the verb. It is used to say that people hold one another's hand. Such as when you say "On a date everybody holds hands."

Agreed! Remember is that "everybody" is treated as a single thing ('it'). Same with "everyone".

It really depends whether this is a command, or a statement. Command: Everybody hold hands Statement: Everybody is holding hands.