Are you kidding? demons don't get pregnant, they don't reproduce that way dude...the majority of demons are born by Larvae of mortal souls in the outer rifts of the abyss, i suggest you to read a couple of stuff:
The book of vile darkness, The book of the damned vol 2, Demons revisited, and there is some info also in Demon's hunter handbook and the worldwound Campaign setting.
Actually, in the case of succubi at least they can get pregnant, they choose not to most of the time, the pregnancy turns into a half-succubus (modified half-fiend) if they bother to carry to term, look in demons revisited succubus section.
they don't reproduce that way dude...
Indeed, it is well known that half-fiends are delivered by the Evil Stork.
As far as the OP's question,
1) there are no rules for this in core Pathfinder material.
2) there are no rules for this in core Pathfinder material.
Given the above, I'd suggest making something up.
Since it's mostly making things up as there aren't really any rules on normal pathfinder material, I'll try my hand at making stuff up.
1) - Succubus have relatively normal humanoid composition body wise, save for a bit tougher maybe, so I'd probably only go as many as a normal humanoid female might. Say 1-2, maybe 3. Any more than that is generally rare, but not at all impossible for normal humanoids. That is however assuming that their anatomy is anything like a normal humanoid females in terms of birth. I haven't read the material so maybe they produces eggs or something and thus there could be more "buns in the oven". But I'd probably just go with 1-3 personally.
2) - The only thing I could think of is magic. In terms of spells in paizo materials, I suppose you could wait until the babies are born and clone them via the spell. Clones are just ice if I recall correctly though, so that may not be what you're looking for. If not, I'd probably just suggest making up your own spell or ritual available in the abyss and run with that. You don't even need to write out the spell as the players are highly unlikely to ever be able to use it. As it'd be custom and just for story, you could make it in the belly or after birth. Whatever floats your boat.
Of course it's really all up to you. As others have noted, you'll need to make it up for your story in whatever way suits it best. Good luck.
Indeed, it is well known that half-fiends are delivered by the Evil Stork.
I know you're being funny and I know I can't (be bothered to) produce a citation, but I'm certain I've recently read some Paizo materials that discuss the provenance of things like tieflings as being the result of fiendish influence rather than impregnation.
But yeah, make stuff up.
1) - Succubus have relatively normal humanoid composition body wise, save for a bit tougher maybe, so I'd probably only go as many as a normal humanoid female might. Say 1-2, maybe 3. Any more than that is generally rare, but not at all impossible for normal humanoids. That is however assuming that their anatomy is anything like a normal humanoid females in terms of birth. I haven't read the material so maybe they produces eggs or something and thus there could be more "buns in the oven". But I'd probably just go with 1-3 personally.
Of course, there are many ways to deal with this from a world building perspective.
One is to look not at what humanoid women 'usually' do, and what they have 'rarely' done. My google-fu is weak right now, but the fact that wikipedia lists the word for 12 at once (duodecaplets)....well then.
Another approach would be to look at the demon as a supernatural creature, and just go crazy with it. I will not go further into that line of thought....because ew.
The final approach I will discuss, and the one that might be the most intriguing conceptually is this- the very nature of demons would prevent more than one being born...alive. My reasoning is this-demons are the very embodiment of chaotic evil, and creatures influenced by that nature without an intelligence to hold back those instincts would take it to the extreme. So, following this logic....multiple babies are conceived, but only one can leave. There can only be one. More butchered references to 80's movies.
So, this approach would have them killing and eating their siblings. Admittedly, this approach would encroach on an already existing race of Abyssal fiends (demodands)... but there are still interesting way to deal with it. What if, in the process of devouring their siblings, some survive (or at least parts of them) and instead become absorbed. That is a relatively easy way to add body horror into this whole experience?
Not sure if you would want to take this route though. I mean, this would dehumanize the offspring to a greater degree than you might have originally gone for, and it might make any moral ambiguity with having to deal with your own bastard child. Although...if you are going to brothels in the Abyss (and you seriously did not use protection? What if you caught mummy rot?), I guess serious consequences and moral quandaries might not be so much of a problem for this character.
What sorta guy is the father?
Is it a fighter? classic pregnancy idd say, perhaps twins, burly ones that grow quick and learn to fight like champs, one in demonic plate armor fused to his skin, the other with a massive axe/sword thing fused into his left arm.
Barbarian? A savage set of quintuplets, they have a strange sense of love for their siblings, and play cruel, games with each other, such as "who can torture the lizard the most before it dies?". Their games are "constructive" after a fashion, invariably harming some 3rd party rather then themselves.
Sorcerer? The demon lord might see the magical blood potential and transmute her into a magic fueled demon forge, not so much birthing demons as producing them en-masse.
Wizard? Ice devil tail and spiked icy spine. When he comes of age he strategically subverts a Kings throne on the material plane and reveals himself as the final villain in a later story.
Rouge? The succubus is slain during a seemingly normal pregnancy, pierced clean through by a massive "dagger" belonging to some colossal demon and propped up on said demon´s ramparts as decor. Spliced on the dagger the demonic pregnancy gestates and transforms the unfortunate mother into something grotesque, winged and taloned.
Cleric? The baby is born as a beautiful human specimen, with no ill blemish on her body, but if you look inside its mouth you will see a burning pit full of red runes and hellish vermin. The hellspawn is born adult, and is set upon the mortal real to spread enticing prophesies and promises to the unvary and the easily deceived, hiding its mouth with a light veil.
Alchemist? The newborn baby boils up to massive size right after birth, explodes in a shower of goo, in the wake of this destruction is left a simple Lemure, a devil. Scorned and ridiculed by its mother and cohabitators in the place of it birth, yet never entirely cast away (thansk to some twisted family pride) the strangely intelligent creature takes up its fathers profession, ultimately adopting a pragmatic, neutral, personality.
Witch? The Succubus, during her pregnancy, gets into a heap of trouble with her lord. To escape she sets up a humiliating summoning contract with a Hag on the Material plane. Shortly after disposing of her summoner, the Succubus starts to develop a classic "Glenn of dark pleasures" with her daughter(s) in some nearby woods.
Gunslinger? The child is born ugly and haunched over like a mule, slowly it grows a nexus of flames grows in a hole in its chest. Once it reaches adaulthood, the Man now stands tall, proud and beautiful, if not for the hellish nest of fire in his chest. In battle he can use this fire as a weapon, shooting bolts of fire rapidly, like gunfire, or in massive blasts, like wizardly spellfire.
Samurai? The Succubus lays fleshy eggs instead of gestating the babies internally, then leaves them to her lord to watch over. Eventually the eggs hatch into adolescent half-fiend men who instinctively swear fealty to their father.
The possibilities are endless of course, feel free to use any of these ideas.
Succubi pregnancies are a matter of canon. They're in the RotRL AP. Females are alu-demons, males are cambions.
Yes, the alu-demon is from Tome of Horrors, but ToHC is a canon source and its monsters have been used multiple times in Pathfinder APs.