If a baby was converted at birth by adoptive parents, and the girl later in life (25+ years) finds her non-Jewish biological father, are they allowed to have any physical contact, i.e. a hug etc. ?
Yes she may. The reason is, although she is considered to be reborn, when she undergoes conversion, however regarding the laws of arayos, she is still considered like the daughter of her physical father. This is because if when they kiss or hug, it isn’t out of lust, rather because of the inborn natural bond between a father and daughter. Therefore it is no different the any father that is permitted to kiss his daughter.
Igros moshe E:H 4-64(1), Shevet Halevi 9-E:H 260, Shut Yoshiv Moshe pg. 190 in the name of R’ Eliyashiv zt”l, Kinyan Torah 5-126.