As far as I know you cannot be born with it. Yes, it is transmitted by skin to skin contact. There are over 100 strains of HPV, over 20 of those involve genitals (including the cervix, vagina, vulva, penis, anus, mouth/throat). Because some strains affect the genitals it is considered an STD.
From what I have read, a baby can be born with it, but it will not effect the baby in the same way as it does say a woman (in her cervix). I believe I read something about it showing up in the lungs, but I could be mistaken.