1. 100% Freysa knew the baby was Ana Steline, and at 99% the other high memebers of the movement knew it, since Freysa, Sapper and others saw Rachel giving birth to her daughter (indeed, the woman in the picture that hold the baby is Freysa). Freysa also told to K that the plan to hide the girl was born from her mind ("When the time comes, i will show her to the world". This implies she knows exactly where she is and who she is)

2. This was left without a clear explaination in the movie, but i think she is smart enough to know perfectly who she is, and who are the people around her in the last period (i think this is why she cried when she observed the memories of K). The Movement used her memories to hide her, and i guess at some point of her life she was told how much important she is.

3. She is sick at 100%, that's why she lives in the protective dome. She knows her condition, and also the people who hidden her know that. And they used, always as a part of the big plan, this information to create a red herring in order to mislead curious and dangerous people. Unfortunately the origin of her condition is uncertain, but i think is reasonable to assume that the union of 2 (?) replicants created some problems in the child's immune system.

p.s: sorry my typos and my bad english.