Received Form 3531 - Box 1 - need original signature

I paper filed form 1040 (since I needed to file forms not available online) but simply typed my name in the Sign Here box. IRS sent me Form 3531 requesting original signature. I am currently not in the US so mailing an original signature to IRS is costly. 

Question 1: Is it ok if I sign (manually) Form 1040 here and then scan and email it to my mail processing agency and they can send it via post?

Question 2: Do I put today's date in the Date section?

Question 3: My State return has the Federal return attached to it. Do I need to also file an amended state return with this "wet signature" Federal return attached?