לז"נ זקני שמואל בן משה ז"ל נפטר כ' אייר תשמ"ט
Shitas Rabbeinu Yonah
Rabbeinu Yonah Shaarei Teshuva Shaar 3:94-95: The Pasuk (Devarim 19:29) states Do not profane your daughter l'haznosah, and the do not corrupt the land and the land will be full of harlotry. Our sages taught (Sanhedrin 66a) this verse comes to warn us not to give your pnuyah (unbetrothed, unmarried) daughter for a conjugal relationship which is not for marriage. "And the land shall not be corrupted" if you do this, the land will be full of harlotry and will make its produce in another place and not in your land. Similarly it says (Yirmiya 3:3) the rain has been withheld and there was no precipitaion, you have had the forehead of a harlot. And pilagshim (concubines) without kesubah and kiddushin were not allowed to anyone except a king, whom everyone fears, and no one will commit adultery with her. Therefore, the relationship (yichud) of a king and pilegesh is like marriage. After pilagshim were allowed to a king, our sages decreed on a bride without the birchos nisuin (sheva brachos) is prohibited to her husband like a menstruating woman (see Kalah 1:1. Shita Mekubetzes, Kesubos 7b mentions this law from Maseches Kalah, but not in the historical context that Rabbeinu Yonah says.)  And behold you have seen the great punishment of one who has a specific pnuyah for illicit relations, because it is written about this (Vayikra 19:29) and do not corrupt the land and the land will be full of harlotry. One who comes on a pnuyah once by a chance occurance (i.e., a "one-night stand," not a relationship) gets makas mardus (rabbinic lashes) (see this post), besides for the great stumbling block and the bad things that happen to those who live with a pnuyah, because she is too embarrassed to immerse due to her mensural impurity in a mikva lest her illicit acts become public, therefore she remains in her menstural impurity [which is a chiyuv kareis]....
Rav Ahron zt"l said the Rabbeinu Yonah holds one receives malkos dioraissa for a common law marriage. I guess he infers this from the beginning of 3:94, that the pasuk (Devarim 19:29) is prohibiting a relationship that is not kiddushin - also known as common-law marriage, so as pshat in the passuk, its punishment is malkus. The Rambam holds there is no malkos midioraissa for this.
The Ramban (Tshuva 284) holds that it is mutar to have a pilegesh but writes, "And, our master (Rabeinu Yonah, to whom this tshuva was sent), in your place warn people against having a pilegesh, for if they knew it was allowed they will be adulterous and break through [the boundaries] and cohabit with them in their state of niddah." So it's muttar but you should not do it. But, is it mutar for an unmarried woman to go to the mikvah? Not really. Shu"t Rivash 425 quotes the Ramban as explaining the Gemara in Shabbos 13b that when a woman will not be allowed to live with her husband, she may not immerse in the mikvah. Any woman who will not be allowed to her husband is prohibited from immersing in the mikvah, and this prohibition extends to unmarried women as well.