I want to know the meaning of "complement of" here.

What does "keep [someone]'s head down" mean? Could you please tell me some examples?

When you "keep your head down" you're trying not to be noticed. This is usually so you don't get in trouble or when a difficult situation arises and you don't want to be involved. Ex: The boss was very mean at my last job. I kept my head down so I wouldn't get in trouble. Ex: You're going to be new in the school! Keep your head down and study hard. Ex: Keep your head down. I don't think he saw you. Keep walking!

What's "consume" mean here?

Here "consume" means to completely destroy, the same way a "fire" would consume something. She's saying that they wouldn't be good for each other, and they'd end up hurting each other in some way. Ex: The fire consumed the house in five minutes. Ex: You'll be consumed by the competition. I don't think you should do it.

Can I say "last one thing" instead of "one last thing"?

The expression itself is "one last thing." "Last one thing" has the wrong word order and would sound awkward if used. Ex: One last thing! Can you take out the trash after doing the dishes? Ex: I have one last thing to discuss with you.

Is "that" necessary here?

Yes, "that" is necessary for this sentence. It is being used as a conjunction to combine the two clauses; explaining what he made up his mind about as a young child. If we removed "that" from the sentence, it no longer ties the two clauses together. Ex: He was so angry that he couldn't be reasoned with. Ex: I purchased the ingredients that are needed to make cookies.

What does "off the hook" mean? What is the origin of this phrase, maybe from fishing?

"Off the hook" is a casual phrase meaning to "no longer be in trouble/difficulty" or when someone is not responsible for something that has happened. In the clip, the man is saying he is "off the hook" to show he is not responsible for the situation that has occurred. Ex. My teacher was in a good mood today, so he let me off the hook for not doing my homework.