"I need to be done by 3:00." Is that correct?
In one episode on Modern Family, two men are repairing a fan together. Their dialogue is like this:
"Let's do this."
"OK. But I need to be done by 3:00. That's when my dad's picking me up."
"If we are not done by 3:00, I'm gonna tie a noose on this thing."

I'm really confused about this conversation. Shouldn't it be "I need it to be done by 3:00" and "if it is not done by 3:00" ?

Question

"I need to be done by 3:00." Is that correct?
In one episode on Modern Family, two men are repairing a fan together. Their dialogue is like this:
"Let's do this."
"OK. But I need to be done by 3:00. That's when my dad's picking me up."
"If we are not done by 3:00, I'm gonna tie a noose on this thing."

I'm really confused about this conversation. Shouldn't it be "I need it to be done by 3:00" and "if it is not done by 3:00" ?

Answer

The words are  informal or casual, but still correct.

Here, 'done' is being used as a synonym for 'finished'.
"I need to be done by 3pm" = "I need to be finished by 3pm"
"If we are not done by 3pm" = "If we are not finished by 3pm".

Answer

“we need to be done by 3:00” and “it need to be done by 3:00” are interchangeable.

“We need to be done [fixing the fan] by 3:00”. 
“[Fixing the fan] needs to be done by 3:00”