Irrelevant detail.
Good luck, nobody can prevent her from dreaming.
Yes, more than just bio page is needed for CRBA.
What does father of the child want?
Does he want the child to be registered as US citizen?
Even if he does all this and registers the child as US citizen, child's mother can pound sand. She cannot come to the US just because her child is a US citizen. Either husband will have to file I-130 for her or the US citizen child can sponsor her after reaching 21 years. Nothing happens without husband or adult child sponsoring her.
It may take many years until her dream of coming to the states to collect $5000 (how, I want to know too?) materializes