Yes, copyright before going to the the studio. Any changes to lyrics will still be covered; melody is probably more important. I have heard horror stories of guys going into studios, their efforts getting heard by others who were then 'inspired' to write something similar. Protect your stuff before showing anyone in the business.

That said, you own the copyright as soon as you write it, the key is having the ability to prove it. *That* is what official copyright in US is all about; having the proof.
The other questions need a lawyer's opinion to have any weight in my opinion..

IANAL (I am not a lawyer) so just take the above as friendly advice.

I do not work here, but the benefits are still awesome
Make your sound your own!