No she's not. She's just their employee at Sugarcube Corner, but she also happens to be renting a room to live upstairs. Pinkie's parents live on a rock farm, possibly with her two younger sister, Inky Pie and Blinkie Pie. :)
unfortunately no, but i think she does look like Mrs.Cakes doesn't she? i think she had a really depressing life before she became......well.....pinkie.