I have two questions

firstly:

i am 27 years old i came to uk at 21 years of age from usa. My mother just became a british citizen by naturalization she is originally born in south africa. She now resides her permanently with my 18 year old sister who also qualifies for citizenship as she came as a dependant on my mother's visa. I came on a student visa and i am currently on the post study visa. I just had a baby born in the uk and my partner is not british and only obtains his indefinite leave to remain in three years time. I am trying to find out if my mother can apply for british citizenship for me as my family is here and i would have no one to go to in south africa?
Secondly does my baby qualify for british citizenship she was born this year in february?