Well, you'll need some document, in order to prove the child's U.S citizenship.
May i ask if you already established the child's U.S citizenship with us?
No, i haven't do that.
Unfortunately, no relevant information is found.
I was wondering, if my documents have another purpose aside from identification?
In fact, they have it for us. Fro example, we may use your U.S passport with double end: Proof of citizenship and individual identity.
Do I need to provide my U.S. Passport even though I lived over seas?
You can show any document that proves you lived abroad for a long time and you don't have a social security number. You could use your previous or current passport, school or employment records, etc.
and for children, do they have to attend personally when asking for a social security number?
If they are older than 12, yes they have to be present during the interview.
and if I have lived in the US what other information do I need to give?
You could be asked for information about the schools you attended or copies of tax records that'd show that you don't have a social security number.
Now, for adults wanting to get the card for the first time as foreign-born citizens?