When we say "Are you nuts" is this slang or abusive line?

FACT! I'm half pistachio (on my mother's side).

"Are you nuts" means "are you mad"Don't use sentences that you asked in front of kids because then your kids will also pick these lines very soon and will have a habit of saying these sentences. Later when the kids grow up, they come to know the real meaning of the sentences which is actually not good, they will realize that they have learnt this from their parents only. So use decent and good language and be a role model for your kids.

Guess you're too young to remember that the original slang "nuts" meant insane or "not quite right in the head."

This may have evolved from the term "squirrely."

There is also the term "nutty as a fruitcake."

These would indicate that the nuts are the type that might be sold by Planters.

The term used in reference to hardware is usually: "having a screw loose" or "a loose screw."

Are you nuts came from nuts/bolts/screws.

Originally people would say you're missing screws in your head if you're crazy. Then it change to you're missing nuts and screws up there. Then it just changed to you're nuts.

This line is always come out of anger although it is not as abusive as it thought to be but it should be avoided in front of kids.