Skin pigmentation & hair falling out

It has almost been a year since the birth of my second child. During my pregnancy I developed darker patches of skin on my face (my skin colouring is fair to medium)... I thought they might dissapear after the birth of my DS but still havnt. Do you think they will go away... or were even caused by the pregnancy? Has anyone else had this problem.

Also 3 months after the birth of my son my hair started falling out and is continuing to fall out. My hair is getting thin... should I be taking any vitamins to help with this? After the birth of my first child I only lost hair for about three months.

If anyone has any advice or suggestions I would greatly appreciate it!