Now the baby is fully developed and has lots of different types of cells. How did some cells become muscle cells and some become skin cells?

Cell Specialisation or  cell differentiation

it's c. (to reduce the greenhouse effect/carbon gasses)

the level of progesterone is low at the pre-ovulatory phase of the cycle but it gradually increases and the levels are high at the luteal phase. if pregnancy occurs, the level of progesterone will be high throughout the pregnancy.

if egg is fertilized and the mother gets pregnant, progesterone starts preparing the uterus for the implantation. it starts building up the lining of uterus and make it hostile of the period of pregnancy.