you can sell your prisoners to the slavers in the shop tab

It all depends on the level of your "relations" with them. The higher they are, the lower a fee they will ask. I dont know the exact values, but off the top of my head, it goes somewhat like " 90 or more out of 100, they will "love" or "worship" you at that point, and if you ask them to join you, they will join you for free. If it somewhere between 75 to 89 out of 100, they will "like" or "love" you but will still demand some money to join you are a servant. It is somewhere between 60 to 75 out of 100, they will "like" you and will demand a lot of money to join as a servant. If its any below that, they will most likely decline your offer.
Most prisoners start from "loathe" you which is somewhere between 0 to 15 out of 100 relations. Talking to the prisoner in court to ask "how they are doing" should raise their relations a little bit - but you can only do this once a day unless you "reset daily interactions" by use of some items, like Cider, for example. You can also raise "relations" by giving them specific items, such as "trinket" as one example, or by feeding them before they feed automatically when their nutrition is lowered.
Those who have "warden" perk will gain relations with prisoners faster. You can also raise relations passively - for this, assign the prisoner to be imprisoned in the "treasure room" with the Keeper character, and make sure that you set them to "socialize". This way, Keeper will talk to them on occasion which should over time increase their Relations.

BUT

By far the easiest way to raise a prisoners "relations" is by having lewd relations with them, and pushing them to the "horny" temp perk - this buff has a 30% chance to increase "relations" by 1 every tick. The thing is, since prisoners are prisoners, they cant, in fact, refuse when the Keeper propositions them to have sex. Servants will only agree to have sex (perform lewd actions) based on how much they like the keeper and how horny they are, and "asking to get lewd" is a daily action too, so you can only ask once. But, with prisoners, they will not refuse, In fact, some "servants" can start from "loathe" relations too, at which points it would take days for them to become friendly through normal interactions, and those would refuse to have sex even if significantly horny, and during these days they will often get into fights and shouting matches with other servants, causing trouble.
Easiest solution is to select such a troublesome servant, go to "actions", choose "emprison" in the "actions" in dungeon management screen (I assume typo, meaning "imprison") and select a jail to jail them in. This turns a servant into a prisoner, and reset their "relations" to 0 ("loathe you"). Then, select yes for them for enter court and go into court. In here, they are bound, they "loathe" you and you can force them into sex with 100% success rate, although they will complain and cry and so on (which makes sense, they are being forced upon). If you want to make them compliant, then I recommend selecting the option to "temporarily release" them, and then select "follow me" - this gives them temporary massive boost to "relations" - it will catapult you from "loathe" all the way to "like". Since they are still prisoners, they still cant refuse your sexual advances. So, have them agree to "get lewd" and select your preferred activity. Now let the keeper and prisoner perform it over and over and over again till the prisoner feels like "worshipping" you - at that point, you can cease to have sex and select conversation option "will you serve me" to which they will gleefully agree. If your court has other servants inside and props like toilet/shower, you might wanna check those props first and harvest all the "bottled" resources first. If you want to go AFK while they perform the acts, I recommend selecting "blowjob" option as that one will not result in pregnancy (unless that is your wish, of course).

So, to sum it up: If you have prisoner/bad servant you want to turn into a good, loving servant, first imprison them, enable them for court, go to court, temporarily release them, ask them to follow you, have sex with them and go AFK for some 5-15 mins or so while they constantly perform the naughty, at which point the prisoner will worship you, stop the sex and ask them in conversation option to "serve you" - court automatically ends and you have a new servant who adores & worships you. This is the most efficient brain washing method in the game that I found so far. Other variations of this method includes the use of props like "milking station" or "lust vaporizer" which will increase the lust of the prisoner gradually if used in the court, so you can make em horny without touching them yourself. Naturally these methods can be troublesome and require more effort, but they are still an option.

Yes. If you enable them in court, and go to the court, you can ask them in conversation "when are you due" - they will tell you the amount of days. The closer they get to that date, the more obviously pregnant they will look (belly swollen etc) - and once the day comes, out pops the baby, fully grown already. They will have the same last name as their parent (I think as their mother, but not 100% sure about that), and they will inherit a mix of genes of their parents, as well as one of the randomly selected genders and races. Additionally, the child will always possess the "virgin" perk trait (naturally). 

Here is an example of what a child might look like:
If a fiend male and human female have a child, the child can be, for example, a human female with the "leg type Hooves" and "fiend wings" despite being of human race, but possess "pale" skin that the human mother has (basically, the child is considered a human, but has many characteristics of a fiend.
GAME issue that comes with the offspring and gene inherition
Now, since "vagina" and "penis" are both considered genes, the female child will likely also possess the penis trait, inherited from the male parent. There is no ingame way I found out how to remove the "vagina" or "penis" trait from a character once they possess one. This means a "female", which is not characterized as "futa" in the game, can still impregnate other females with a child, or a male with vagina trait can be impregnated. The only way these traits can be removed is by quitting the game and forcibly adjust them in a "save file". Save files can be found in the game folder under Dungeon Keep Her_data in folder "saves" and can be edited with "notepad" - inside, use Ctrl + F to enable "find feature", type the name of the servant and find the correct one, then use find feature to find the "penis" or "vagina" gene trait, and remove it, save the file and restart the game while loading this file. You can also use this to edit the characters forcibly with perks you might want (for example, I give all the servants and prisoners  I plan to keep the "Barren" perk trait, which makes them unable to have children. It basically acts as a contraception since there is no way in the game to brew a potion that would do the same. If I wish to remove it later on, it is as simple as using a red crystal on them to remove this "detrimental" perk.