As far as I can remember the books never said that women couldn't be Witchers, it's just that all the Witchers mentioned in the books are male. It could be easily hand waved by CD Projekt Red as a female protagonist being an exception to the general rule that Witchers are men. It is nothing that skilled writers couldn't write around. In fact the Polish movie has already done that. There was an entire school of female Witchers in that.
Yeah, well I wouldn't call the TV Series/Movie an exactly good source for inspiration or skilled writing, since it was so shitty that even the original author (Andrzej Sapkowski) hated it. Samurai Witchers anyone? 
And female Witchers are a different issue altogether. They seem to be really uncommon/non-existent in the book and game canon which gives me the impression that Witcher schools simply don't take/accept them. Meaning if a Witcher found an orphan in a ditch and she was a female, he'd mostly likely just leave her there, as opposed to a boy.. the Witchers probably don't feel comfortable risking women and that men are more expendable. Call it medieval misogyny if you want. 
So it's not that a girl couldn't become one, it's just that a girl was never "given" the chance and it seems like the devs and author himself (if his new Season of Storm book is anything to come by) still don't really feel like changing it.
Of course, the could try to write a possibility for a female Witcher, but I am afraid it would turn her too much into the "special snowflake" kind of trope.
Then again, we haven't yet seen anything like this from CD Projekt so far, so it could be good. Who knows.
As for new apprentices...a new protagonist wouldn't have to be a new apprentice. As I mentioned in my earlier post, there are existing Witchers that don't appear in the books or the games. At the end of TW2 Letho briefly mentions two surviving Viper school Witchers who never actually appear in the game. Either one of those could quite easily be used for the protagonist of a new game, and because they are only briefly mentioned, there is plenty of room for character customization. Just as with Geralt the player steps into the boots of an experienced Witcher, the same could also be true with a new protagonist.
Sounds good. Either that or perhaps like my original idea about the different Witcher schools with a semi-custom Witcher for a spin-off series or something along those lines. Something akin to Alpha Protocol or Mass Effect in terms of customization, backstory (maybe a bit more), while still retaining the strong writing for a pre-determinted, semi-established character.