Do I need to sign the 1040 if I mail the file? What should I do with the "Paid preparer Use only"

Yes, you need to sign and date your 1040 and include all income documents such as W-2's that have tax withheld. You do not complete the paid preparer's section.

Yes you need to sign it to mail it.  There is no paid preparer.  Turbo Tax is a self prepared return.