Parent
Within a family, a parent generally served as caregiver. Oftentimes the immediate ancestor of their dependent(s), one who engaged in parenting might also be termed a mother, father, or grandparent.
This took many forms. For instance, while K9 Mark II understood that "mums" were commonly "female progenitors", (AUDIO: Legacy of Death) Sarah Jane Smith first became a mother by adopting a Bane human construct, Luke, rather than through any kind of reproduction. (TV: Invasion of the Bane, et al.) Depending on the species, a child could have three or more parents. (COMIC: Meet the Fam! )
As Vedirioi, a Torcaldian, put it, humans "specialised in one or the other", and were generally confined to being mothers or fathers. Torcaldians, who could play either role in the production of offspring, did not pay very much attention to gender or its assignment. (PROSE: The Ruins of Time)
As a clone race, Sontarans had no parents. (AUDIO: A Photograph to Remember)
A tribute for Clive on Who is Doctor Who? mentioned he was a loving father and husband. (PROSE: Dummy Massacre)
Both the Doctor and Davros considered the Kaled to have been the Daleks' father. (TV: The Witch's Familiar)
During the 2010s, Coal Hill School hosted "parents' evening" where parents could question teachers about the academic performance of their children. (TV: The Caretaker)
The Doctor
The Doctor had, in the Tenth Doctor's own words, been "a dad" (TV: Fear Her) and "a father". (TV: The Doctor's Daughter)
The Nine knew that there had once been a "lucky mother" involved in the Doctor's parenthood. He also acknowledged that the Fifth Doctor might well have parented a child with another father as coparent. (AUDIO: Relative Time)
The Tenth Doctor became Jenny's father through progenation, (TV: The Doctor's Daughter) while the Eighth Doctor adopted Miranda Dawkins. (PROSE: Father Time)