why did they gender swap these characters to women
originally the roles of Shirou and Arturia were the opposite genders as the original concept for Fate/Stay Night (now as Fate/Prototype) had Ayaka Sajyou as the Master of Arthur with Gilgamesh also vying for Ayaka's heart.
however it was Takashi Takeuchi, the artist of Fate/Stay Night who convinced Kinoko Nasu to change Arthur's Gender
Kinoko Nasu's original story of Fate, Saber and Shirou were opposite gender to now. Takashi Takeuchi convinced to Nasu to change the gender of Saber but the essential theme had not been changed, it's the story about legendary heroes and "a boy meets a girl."
Source: Saber (Fate/Stay Night) > Development > Creation and Conception
In regards to Mordred, originally when Mordred first appeared in one of the Type-Moon Character material books Kinoko Nasu originally hadn't decided what Mordred's gender would be until Fate/Apocrypha and originally was siding on keeping Mordred male, however after Takashi Takeuchi put the idea of adding Mordred into the lineup it was thought 2 feminine male characters would be too much
Mordred first made an appearance in Type-moon's Character material book, with Takashi Takeuchi responsible for the character design. At that time Kinoko Nasu hadn't decided on Mordred's gender until Fate/Apocrypha. It was Takeuchi's idea to put Mordred as a new addition to Fate/Apocrypha. As Saber of Red Mordred was originally going to be male like the legend, but it was thought that having two male characters look feminine, the other being Rider of Black, was too much.
Source: Saber of Red > Development > Creation and Conception
Nasu: "Mordred is a girl, definitely. A man with that sort of outward appearance is... well, I guess a certain kind of person would consider it a prize, anyway.1 (laughs)"
Higashide: Saber was originally going to be male like the legend, but it was thought that having two male characters look feminine, the other being Rider of Black, was too much.
Source: Saber of Red > References > Citation 4: TYPE-MOON Ace Vol. 8 - Fate/Apocrypha interview with Yuichiro Higashide & Nasu Kinoko, p.080
What's Mordred's gender?
As for why, in universe, Mordred refers to herself as Arturia's "Son" she could be well aware of her own legend. the Arthurian Legends in the Nasuverse is still closely related to ours and in Fate/Stay Night when Shirou discovers Arturia's identity as King Arthur he does talk about how the Legend of King Arthur wasn't clear on who the King was pointing out that some legends suggested that King Arthur was a group of people.
since we know that when a Servant is summoned they are given extra knowledge to adapt to the time period (ie. Arturia's abilities to ride a Motor Bike, not thinking that the Airplane she flew in on was magic) we could suspect that Mordred is made aware of her Legend.
There is also the fact she wanted to be King and the King is generally the Son of the previous King but aside from that still male. Merlin helped create the illusion Arturia was male by making into a
futanari psudo-male so she could conceive a child with Guinevere so Mordred may keep saying "Son" to keep the idea and she can replace her "Father"
There is also the fact that she abhors any discussion of her gender and displayed clear killing intention even towards her own Master, saying with no uncertainty that the topic is never to be brought up before her. though haven't not seen Fate/Apocrypha or read it properly i do not know what the discussion entailed and what she abhors about it (is it people referring to her as a woman or man? or that she could be like Nero and doesn't consider Gender an issue)
Out of Universe, we can probably speculate that either
Takashi Takeuchi just has a thing for it which is why so many of the Saberfaces using Arturia's design are Gender Reverse from their historical basis (Nero, Okita) and is projecting that in the Nasuverse (do we really believe he didn't suggest Female Mordred for the Fate/Apocrypha lineup when putting the idea into Kinoko Nasu's head)
Simply people like cute girls. Taro Yoko, the creator of Nier: Automata said it himself when being asked why he designed 2B like he did.
Medea Takashi loves how cute Arturia looks and obviously the fans love them too, more so when you consider that the manga's target demographic is Shōnen and Seinen which are both male audiences which we can probably attribute to having been the same for the original Eroge Visual Novel and character design often is influenced by target audience (ie. why most Vampires in female oriented works (Kaname Kuran in Vampire Knight, Angel and Spike in Buffy and Angel) are handsome men)
1: i believe he's talking about Takashi here give his noble phantasm