What would this look like in terms of social structure, class division, genocide v. control of scarce female populations, polygamy v. monogamy, cultural and linguistic change, etc.?
Slavery of women, sexual and otherwise.
The premise that powerful men could slaughter all the males in another culture and capture all the females is entirely feasible; although the only reference to that I know of is a story of Moses going to war in the Old Testament, which may be legend, or a fictional exaggeration of an actual conquest. In that story, Moses kills all males (including infants and children) and all non-virginal females, and then gives away the remaining virginal females to his conquering soldiers as slaves (for sex or labor by the rules of the OT) as the spoils of war.
In general, the original social structure, and likely religion and culture, would collapse. To the women, the invaders would be men that just brutally murdered their sons, husbands, brothers and fathers and lovers, all the males they loved in any way. Probably their armies, political and religious leaders and police force, since in most cultures these fields are led primarily by males. (Also, historically, utter defeat of a people often causes their religion to decline and be abandoned. Not always, but with all males dead I would presume so.)
The new social structure would likely be males-in-charge and women as second class citizens, breed stock for the males. After all, that is how it began, and chances are high the women are coerced into sex and pregnancy just because they are the conquered victims, and as humans we can expect them to be unwilling participants after invaders have murdered every male they love. The invaders would be regarded as brutal monsters; and their crimes (from the women's POV) would never be forgiven; I doubt many could move emotionally from the hatred and grief they feel to fondness for the men that caused that. Perhaps those too young to understand what happened; e.g. age five or less, could be raised without the hatred and grief, but they won't be able to have children for nine or ten years. In the meantime, I presume any women past puberty would be raped, effectively sex slaves (and labor slaves) for the conquering males.
As far as linguistic changes, conquerors tend to force their language on the conquered. For example I believe (without research) that the primary language of American Indians is now English, and I have read that most of their children are no longer fluent in their native language, and some don't know any of it. The same is true of African slaves born into American's Slave South. Although it doesn't apply in this conquered scenario, even when voluntary migrants join a new culture, their descendants (children, grandchildren, etc) lose more of the native language every generation. (And as you can see even in modern America, many citizens here advocate for forcing migrants to become reasonably fluent in English.)
But that is as far as I think we can plausibly extend the analysis, the other questions have no answers.
As far as how these conquering males share the females, that will be quirks of their own culture and/or religion. They may be egalitarian and share them equally. They might assign women to men by lot. It may be meritorious. The conquerors may have some hierarchical order, by age or 'royalty' or scars in battle, so they make their selections in some hierarchical order among themselves. e.g. their King gets first pick.
They could also be either polygamous or monogamous. If there are many women conquered, polygamy would seem required to impregnate them all, if that is indeed what the men want to do (it might not be, the conquerers may not be in a big hurry to create many infant mouths to feed and protect).
Although I am not aware of a historical precedent for conquerors, we could even posit the fictional conquering men are not that possessive of women and do not closely track paternity. There is historical precedent in the 'hippie' and 'flower children' culture of the 1960's and 1970's, in which many young women were casually promiscuous and had enough sexual partners that paternity, when pregnancy resulted, was uncertain. To an extent this remains true today and many young men may be fathers without knowing it. The father of my sister's first child, which she bore at 15, never did know he fathered a child. So the fictional conquerors' society may be such that paternity is not important to them, and exclusivity or a permanent partner for sex is not considered desirable.
For an example (intended only as an illustration and without any endorsement by me), consider a brothel: Women are on display and men choose amongst them, pay for their services, have sex, and depart. If such women become pregnant, paternity is uncertain; many such women have intercourse multiple times a day and the father of a child could be one of dozens.
Such a coerced brothel model may be the cultural norm for the conquerors; so neither polygamous or monogamous. The children, after nursing to the age of two or so, could be separated into males and females, and the males then raised by men to be warriors (Spartan style), and the women raised to be either domestic labor or brothel residents.
All of which is offered to say this question is too broad in many respects. The conqueror's culture and social structure will generally prevail, including the fact that they go forth as an all male group and conquer! And kill all males when they do. Given that dynamic, the subjugation of women into coerced sex and labor seems inevitable to me, but a writer would be free to invent many alternative realities within that circle.
Response to first comment:
4000 million men, divided by 10 million men, is a 400:1 ratio. Note that military superiority is a given, for such a defeat, the means is not an issue in this question. With reference to human females, the ideal breeding age is about 15 to 30; 15 yrs in an average 75 yr lifespan, roughly 1/5 the females: Thus about 80 per conquering man. Many kings and emperors have had sex more often than daily, especially when young, a man could easily impregnate 80 women within a year, if desired.
However, the actual global population rate is about 1.1%. Eliminating living males, that would be 2.2% of the conquered females. If there were 4 billion such, the birth rate should be 88M children per year. Given 10M men, they each would need to father about 9 children per year in order to sustain the current population growth. That is about one per six weeks, which is entirely feasible. (In the USA, the population growth rate is only 0.7% annually, so it depends on the culture to a large extent).
As for a "fetishistic" focus on the subjugation of women, I find any such subjugation by gender or race repulsive, but I am also not in denial about the reality of the past of humanity, where such subjugation was common for nearly all cultures until the last few centuries, and often enshrined in law and religion. That was reality, and the further we get from it the better. Good riddance. This particular question asks about precisely that dynamic, the OP explicitly states his opinion that it happened, and asks if it did, what are the consequences?
Do not forget the nature of this forum, I do not need to cite any historical references to give my opinion of the logical consequences of some posited fictional scenario!