The whole Vain Sorceress thing makes no sense. Almost all girls with Gift that are sent away by their parents are either disfigured or from extremely poor families. Or both. This is explained that no-one wants to sent away their daughters, because that means no heritage. But in given settings women don't inherit anything, are a trading good in marriage and are expected to do nothing more exept being good wives and mothers, no matter what is their social status. And marriage means dowry. It's also common knowledge that people with Gift are in almost all cases sterile, so there is no real chance that your daughter will give birth to bunch of kids. On the other hand, magic users have access to trendemous power, both literally and by means of diplomacy and wealth. So if everyone is so pragmatic with family management, the best way to use your Gifted offspring is actually sending it away for magical training (which goes for free and you are paid for it) and then raking actuall profits from having a sorceress in your family.
None of this happens, because author needed a steady pool of Broken Bird characters.
The issue of infertility is described in unclear terms. On one hand, many characters react as if it was magic itself that was the cause of infertility. On the other, it was stated outright that — at least — one very influential magician called for forced sterilisation of magic adepts, specifically to prevent uncontrolled proliferation of magical talent. Regardless of any other conclusions (or cans of worms to open), it implies that magic doesn't cause infertility in every case.
The wizard students have it hammered into their heads that they're supposed to be above familial or even national loyalties. This, presumably, severely hampers the milking of profits, especially as young wizards don't have a whole lot of push. On the other hand, in light of Season of Storms it still doesn't explain everything.
Most people who go into magic academies never become powerful sorceresses, leaving them with rather low-level administrative jobs at best; high level magical talent is rare. Also, there is some major prejudice against magic and the magic users' internal hierarchy is completely separate from the family-based and feudal power structures that most people in this world understand as meaningful.
Magical traning isn't free. At least in Aretuza you have to pay good money for each year, probably more than would cost for a dowry. Besides it was stated that when a girl finishes her magical education she no longer holds loyalties to her family, so it's unlikely that a family would benefit more from sorceress daughter than marring her off.
If you happen to have a magically talented or sensitive offspring, not only magic users will pick that kid and put in school, they are going to pay for it if you can't afford it. In short - it's not your financial burden. The whole assumption people are going to forget about their family just like that in a setting that virtually runs on family connections is just... it simply doesn't mesh together.
Population. It's stated numerous times that humans came to this land at some point in the past, sailing from somewhere. Word of God says that humans landed less than five centuries in past, in group of less than ten thousands. That means Writers Cannot Do Math combined with Artistic License – Biology - human population in short stories (which take place a generation before saga) is counted in millions. To actually reach so high numbers humans would have to literally mate like rabbits with zero fatality before reaching maturity. To made this worse, there were two huge wars during that period - Last Stand of elves and war known as Falka's Rebellion, the second one being a rather recent blood-bath spanned across nations. Not to mention smaller wars, diseases, famine, monsters...
If the population doubled once per generation, which is nothing special in case of medieval times with around four kids reaching adulthood, you can easily get this or an even much higher number.
IIRC, it wasn't ever mentioned that the First Landing was the only landing. The Connection of Spheres made it possible to directly sail from the Old World without using portals or other magic, and it's entirely possible that the colonisation continued for decades, if not centuries. I might've missed some cue or Word of God, but it appears that the population continued to grow due to resettlement in as major way as simple breeding.
The elves inadvertently helped the humans considerably in this respect. There was a huge amount of crossbreeding between the two species in the early centuries, until it started to get clear to the elves that humans were outbreeding them from the gene pool with their faster reproduction rates, half-elves giving way to quarter and one-eighth elves, who differed little from ordinary humans. It is mentioned several times in the stories that nearly every human in the setting has at least one elvish ancestor in their family tree.
We know that the elves somehow opened a cross-world portal and evacuated from the dying world. But how exactly did they manage that? The elves from another world can only manage short jumps, and probably couldn't help with such a big project.
The older elves had access to the powers of the Elder Blood. It's an essential plot point that Ciri is theoretically able to create long-term gateways that would allow the Wild Hunt to evacuate ahead of the White Frost. Elder Blood was a rare trait and the elves had a bitch of a time recreating it later on.
In The Blood of Elves, Geralt takes an elixir in preparation for a fight that increases his combat prowess but has the detrimental side effect of lowering his rationality and reducing his control over his emotions. When he sees a group of assassins approaching, he notes to himself that he doesn't want to kill them but that if a fight starts he will have no choice, due to the elixir's effect on his mind. And indeed, he is so overcome with anger during the fight that he butchers all of them in gruesome ways. However, before his fight with the striga in The Last Wish, he took several elixirs that had a similar effect on his combat prowess but obviously without the drawback, as he maintained strict control over himself during the course of the fight. He was very careful to hurt the striga without causing any lasting injuries. So if Geralt has elixirs that can enhance his abilities without robbing him of some of his mental faculties, why didn't he take one of those instead of the one he used in The Blood of Elves?
As I recall, the elixir he took in The Last Wish only enhanced his senses to a supernatural degree, allowing him to sense the Striga's position perfectly at all times. He did the fighting itself with his own skill.
Why, in Lady of the Lake, do Geralt and Yennefer decide to commit suicide? I mean, I get that they think it's Better to Die than Be Killed (and given Nilfgaard's methods of execution they're probably right), but Yennefer is no longer wearing her Anti-Magic shackles, so she could just teleport them to Kaer Morhen the instant the guards looked away. Is it just a case of Honor Before Reason, since they promised to follow through with it?
And what would they do next? Because for sure not living happy ever after. Ciri stays with the emperor, no matter what they do. And the emperor wants them dead, but in his courtesy he's leaving behind a dagger. So no, they have no reasons or purpose to escape, since there is nothing left for them to live for.
And now he turned around and said that they lived after all, even if the games are in a separate continuity.
So why exactly does Geralt grab his sword by the blade for some finishers, and somehow kill his enemies with the shaft? It doesn't even qualify as Rule of Cool because it just looks plain weird and should logically hurt his hands, given how hard he swings it...
Grabbing the sword by the blade is a real swordfighting technique. The guys who made the combat choreography for the game were well aware of it. Apart from Rule of Cool, it makes perfect sense against the tough opponents — in Real Life this kind of stuff was meant to get through full plate armour.
Some medieval longswords even have an unsharpened portion of the blade called ricasso, which is specifically intended to be grabbed onto in combat and used for thrusting and heavy cleaving attacks against a heavily armored opponents, much like a polearm would've been used.
Holding the sword by the blade is a perfectly acceptable fighting strategy, especially if you have hand protection. Even a leather glove would be more than enough to hold the sharp edge of a sword long enough to swing it around and use the hilt as an impromptu hammer.
Ok, so, Dudu. The man's name is a homophone for a euphemism for feces. Was this intentional as a low brow joke, or is it not so unfortunate a name in Polish?
It is an unfortunate case of not translating a name which has a different meaning in a different language. In Polish it doesn't seem to have any particular meaning (besides sounding quite silly albeit rather accordingly for a halfling); it does, as a matter of fact, exist in some countries as a real name.
Dudu, along with Duduś, is a diminutive from "David" in certain parts of Poland
Dudu's full name is "Tellico Lunngrevink Letorte, Penstock for short, and Dudu to friends."
Why do Geralt never use Signs in the books? I understand he probably can't spam them like in-game, but I don't seem to recall him using one even once.
He uses them infrequently, more in short stories than novels. Perhaps he is used to the swords as default choice and just mostly lives by without Signs. At one point he implicitly states he needs the medallion to cast Signs, which makes for a simple answer after he loses it.
At the end of Baptism of Fire, it's noted that Geralt's signs are not as effective as he hasn't had access to his usual array of potions which boost his magical ability.