My hospital let us sign everything there, they had their notary and she then took the papers before we left and makes them in for us! Definitely ask your hospital:)
Yes u sign the papers there at the hospital. U don't actually get the certificate until about 10 days later u can go pick it up. U just get a copy verifying who the parents are etc.. (just like a birth certificate )
No they give a paper with addresses of where u. Can get it...u will get a paper with all the info at the hospital