Is your child a u.s. citizen
no
you need to tell Social Security so that your child can get a corrected card
Good to know. Another thing  what other documents do I need ? What documents do I need to show ?
To show proof of your new status we only accept the following documents:U.S. passport ;Certificate of Naturalization N-550/N-570 ;Certificate of Citizenship N-560/N-561 ;Certificate of Report of Birth DS-1350 ;Consular Report of Birth Abroad FS-240 , CRBA
Are there any other documents that I need to show?
You are also required to show us your I-20 Certificate of Eligibility for Nonimmigrant Student Status.
Do I need to prove that I'm still a student?
If you are an F-1 student we need a status letter from your school identifying you as such.
Do I still need to keep my immigration documents?