So here's my first idea. Feel free to pitch in with other ideas.
Both girls are going to focus a bit on maxing out (level 10) their skills that are approaching that point, while also improving the skills that will be useful for their expected futures.
For Illya, this means getting better at politics so that she can better perform her duties as Second Owner, improving her physical condition to help counteract some of her body's problems OR make her better equipped to deal with the pain of any future treatments, and making her start learning English because international politics are going to be pretty important for her down the line.
[X] Illyasviel: Community Connections
[X] Illyasviel: Physical Education
[X] Illyasviel: Studying (Mundane)
-[X] Illyasviel: English Language
I'm not quite sure on Illya's event though. Both political options are solid choices. On the other hand though, making Hayate help her out with paperwork would likely lead to her actually letting Hayate know that she's come to approve of the Shirou/Hayate pairing because she thinks it will help curb Shirou's recklessness.
That's especially relevant considering that Shirou's locked in event reveals that his Harem Protagonist trait is finally rearing its head in full. Some encouragement from Illya might push Hayate towards officially claiming Shirou for herself before all those other maidens try to seduce him.
[ ] (Illyasviel) …spent a significant amount of time working with the local leaders to insert herself into Uminari's local politics.
[ ] (Illyasviel) …spent a large amount of time working with the immigrant leaders to insert herself into Uminari's immigrant politics.
[ ] (Illyasviel) …grudgingly pulled Hayate into helping deal with the large amount of paperwork that she had received.
As for Hayate, Arithmetic and Biology are in because she's nearly maxed those, improve her Influence so that she can better assist Illya in cleaning up the family's messes, and Moonlit Knowledge because it's become an integral part of politics.
Beyond that, Magecraft Theory and Biology are both potentially useful for helping her partially overcome the limitations of her permanent injuries, and both Magic Theory and Moonlit Knowledge will help her detect when Shirou is planning to do something stupid (so that she can coerce him into making a saner plan). Sufficient theory could also potentially let her use Formalcraft (which does NOT require Circuits) to set up a Prana Transfer Ritual in the future.
[X] Hayate: Community Connections
[X] Hayate: Studying (Magecraft (Knowledge Only))
[X] Hayate: Studying (Magecraft (Knowledge Only)) (2)
[X] Hayate: Studying (General Moonlit World)
[X] Hayate: Studying (Mundane)
-[X] Hayate: Arithmetic
-[X] Hayate: Biology