I130 Qs

Honorable pijiang, i need your help please.

1
I did a name change (add middle name) during naturalization interview, but did not think about consequences. Now for I-130, the instruction says
"What If Your Name Has Changed? If either you or the person you are filing for is using a name other than shown on the relevant documents, you must file
your petition with copies of the legal documents that effected the change, such as a marriage certificate, adoption decree or court order."

I don't have a thing except the naturalization paper. Do I need court order?how?

2
is baby's I-130 separate, or going along with mother's I-130? Or in more practical word, do i pay $355 or 2x$355? I indeed read the instruction, but found no answer.

Thanks a million