First, pregnant women, menstruating women, and warriors in preparation for hunts/battles did not engage in sex. These things "involved strict rules" because of their connection to blood, which the Cherokees understood to be "life" and "spirit" (James Adair; Theda Perdue). Personal autonomy for women was akin to modern, U.S. women, in that they were more-or-less free to hump whomever they chose, as long as it wasn't incestuous. Cherokee historian James Adair also understood Cherokee women to be allowed the honor of promiscuity, noting that there were no punishments for adulterous women. In fact, most Cherokee men wouldn't argue over adulterous women because it was deemed to be "beneath" them (Louis-Philippe).

Sexual encounters would, indeed, occur in the beanfields and other places of a relatively private nature (Purdue).

Sorry, in a rush, perhaps I'll stealthily edit later.

Edit: I really recommend Cherokee Women by Theda Perdue. She's one of the top scholars in this field and, sadly, gender studies is relationship/sexual studies.

"When a young man had chosen a girl he wished to marry he would kill a deer and bring an offer of deer meat to the home of the girl he was interested in. If she chose to marry him, she cooked the deer meat and offered it to him. If she rejected the deer meat, it was assumed to be a denial of this suitor."

Cherokee were matrilineal, meaning children were NOT part of their father's family. This is a very foreign subject to most modern "Western" people today. Your mother's brother was basically your father and the most important person in your life. In a way your biological father was just the person that happened to be having sex with your mother. Many cultures with this matrilineal kinship system do not recognize the role of sex in making babies. In Melanesia for example, they traditionally believed that the fertility of the ocean is what impregnated a woman, and explained that children sometimes looked like their mother's husbands, because the child will take on the form of those nearest to the mother while it was developing in the womb. I'm not sure if this holds true as much in Cherokee society however, as there were strict laws against incest, and they recognized marrying someone from your biological father's clan as incest, as well as from your mother's clan. The Cherokee people were divided into 7 clans: "Wild Potato" "Long Hair" "Deer" "Blue" "Wolf" "Bird" and "Paint." Every village was made up of representatives and households from each of these 7 clans. So in theory, everyone would have 5 clans to choose from when choosing a husband or wife.

According to Charles Hudson's 1976 book The Southeastern Indians, drawing from James Mooney's ethnographic work, in general in the region a young man would send his mother's sister to speak to a young woman's mother's sister. The girl's mother's sister would speak to the girl's matrilineage about the idea, often without telling the girl. If the matrilineage liked the idea, they would send word back to the boy's matrilineage.

However, although they arranged the marriages, the girl had final word, and her consent was required.

"Southeastern Indians' favorite places for sexual episodes were corn cribs, corn fields, and bean patches." (Page 198).

Polygyny was widely practiced throughout the region, although the permission of the first wife was required. Divorce existed and could be initiated by either party. Cheating was frowned on and punishable among the Creeks (neighbors of the Cherokee), while the Cherokee allowed both women and men relative sexual freedom of lovers, although women could not marry multiple men or keep concubines. (page 200-201).

Since others have talked about the Cherokee already, I'll look north to their cousins on either side of Lake Ontario--the Wendat (Huron, north of the lake) and the Haudenosaunee (Iroquois, south of the lake). Barbara Mann's Iroquoian Women is my principal source here.

Beginning at puberty, boys and girls were allowed to court as they pleased and often had many suitors. The early French missionaries in the area, like Le Jeune and Sagard, bemoan the sexual liberty that teenage Iroquoians enjoyed (provided the partners from of differing clans). Unfortunately, Mann has a fairly lengthy discussion analyzing a long song beginning on the bottom of page 98, which would have been quite useful for this discussion if it weren't almost certainly wrong. She's quoting Montaigne here, and Montaigne's famous "savages" were almost certainly Tupi from the French Antarctic (southern coast of Brazil today) rather than any Iroquoian people). I figured I should mention that in case anyone else happens to read that portion of the book. Her description of Iroquoian courtship might still be accurate here, but its erroneous to foist an Iroquoian interpretation on the love song.

The late teens and early twenties was the time to start settling down. The Clan Mothers in charge of each longhouse set about negotiating arrangements for potential marriages. The young woman was consulted on which of her various suitors she preferred, but she was never pressured into a marriage unless she was pregnant and intended to keep the child (abortion and adoption were both options available to a women when traditional contraceptives failed). Even then, her would-be husband would still be a suitor of her choice rather than necessarily the biological father. She was not obligated to name the father, though men regarded it as a honor to be recognized.

Once the young woman named a potential husband, her Clan Mothers made the proposal to his Clan Mothers. Unless he was vehemently against the union, his Clan Mothers expressed their consent by presenting the woman's Clan Mothers with gifts. At this point the couple entered into a trial marriage that could last up to several weeks. For most of this time, the man lived in the woman's longhouse, though he would occasionally return to his own. The woman's Clan Mothers observed their interactions and sought to ensure their eventual marriage would be a long-lasting union rather than a temporary fling. If things went poorly for whatever, the woman's Clan Mothers returned the young man and the gifts he had brought along with him.

However, if the young couple passes the Clan Mother's tests, they progress to a full marriage. The woman's longhouse prepares a feast and the celebration takes place in the man's longhouse. Afterward, the new husband and wife lived in the woman's longhouse and the man was thereafter under the authority of his wife's Clan Mothers. As it was the Clan Mothers' duty to settle disputes among the residents of their respective longhouses, it was also their job to settle any marital problems that might arise between a wife and her husband--which included forcing a divorce in circumstances including infertility, incessant arguing, domestic violence, ineptitude. Either partner might petition the Clan Mothers for a divorce voluntarily and would usually be granted one unless children were involved, in which case only extreme situations warranted a divorce.

Children were the only real obligation of the marriage, and monogamy wasn't a necessary part of the arrangement. For men, a common extra-marital affair might happen with a Hunting Wife, a woman who accompanied a hunting party into the countryside. Hunting Wives were usually women who decline the usual societal roles of women, and didn't want regular husbands, children, or Clan Motherhood. The wife often found her husband a Hunting Wife, so she wouldn't have to accompany him out on his long journeys herself. Women could enjoy extra-marital relations themselves, and famously among the Seneca, they might choose to have multiple husbands (into the 20th Century, it seems).

As for third+ genders, that's not, to my knowledge, a thing among Iroquoian societies. I already mentioned the Hunting Wives defying the usual gender expectations of women; there were also men who became honorary women and served on the Clan Mother's Council (usually as intermediaries between their councils and the men's councils). But such people weren't seen as outside the woman / man gender dichotomy. Third+ genders are much more common west of the Mississippi than east of it

Regarding gender, I have seen a few mentions of allowing men to live as women, but they are rare and I can't give proper citations for that. As for dating, I do have a book "The Woodland Indians of the western Great Lakes" which is a bit old and mostly covers Algonquians, while the Cherokee were from the Iroquois language family and further south, but I can offer some quotes from the short section on courtship:

"Most marriages were monogamous, but polygyny [multiple wives] was sanctioned, and an important man could have two, or rarely, three wives."

"When he called on the girl in the evening, he always talked to her in the middle of the lodge, with all the adults nearby. 'Courting flutes' were popular, but the girl could not leave her lodge when she heard one being played."

"As the youth grew serious in his pursuit of the girl, he brought her parents a deer or some other animal he had killed, an indication of his ability to provide for a family. If he was asked to stay and partake of the meal, he was assured of the parents' approval and could come and go more freely than before. The Potawatomi youth brought the girl a blanket and if she allowed him to put it over her shoulders, it meant that she agreed to marry him."

"Marriage involved no formal ceremony, the couple merely going off by themselves for a few days."

This all fits with other things I've read and heard, so I have no reason to doubt the general drift [although that counts as anecdotal].

While not Cherokee, I've had some experience with early North Carolina History and the Tuscarora tribe. I suspect that a good historian to consult on the subject of sexuality and American Indians in early eastern Carolina is Rebecca Seaman of Elizabeth City State University. I remember at the New Voyages to Carolina conference held at East Carolina University in 2012 her presentation on interpreting the dead left by American Indian attacks as in 1711 described in a letter from Major Christopher Gale on November 2, 1711 and what that said about the relations between Europeans and American Indians. I remember in particular how she described that Europeans would come in and intermarry or just have a short period of relations with American Indian women to help set up trading networks (with said women sometimes being treated rather badly) because of such things being traditional among American Indians. The Europeans would do this and sometimes go as far as demanding it, but in contrast would refuse the same treatment for their male American Indian trading partners and European women. So, Rebecca Seaman interpreted the line from the letter the following line about Mrs. Nevill being, "...set upon her knees, and her hands lifted up as if she was at prayers, leaning against a chair in the chimney corner, and her coats turned up over her head," when found dead after these attacks as American Indian commentary on at least two points. One, they were fed up with not being allowed to intermarry with European women (and fed up with the European double standard on the subject) and they were also showing disrespect for the European's Christianity.

Not sure if it's exactly what you all are looking for, but it is about Native American sexual relations - but in relation to early European settlers.