Why is Illya able to survive firing Excalibur when HF!Shirou couldn't? It's because unlike him, she actually has the prana reserves to use it! Their differences in magical capacity spell the difference between an effective Wave Motion Gun and a Suicide Attack. This actually fits well with Archer's own explanation in Unlimited Blade Works.
Why does this Illya differ so much from the character from Fate/SN? Because she is a surrogate, while Chloe/Kuro is the suppressed original. Kuro is ruthless, calculating, and a powerful mage. Just like the little girl who summoned Berserker during fifth Grail War and controlled him flawlessly. No wonder she reacted violently when Illya called her a second-hand clone.
Why does Illya throw Kanshou and Bakuya at Saber Alter's Excaliblast instead of utilizing Rho Aias? Simple, the two are magic resistant. Archer demonstrates this nicely in the main series, wherein he manages to deflect Caster's A-ranked spells using the two.
Given that Kuro also feels anything that Illya does, shouldn't that cause...interesting effects during the Intimate Healing?
Actually explored in one doujin. The results were... interesting so say the least.
If Shirou Emiya is Miyu's brother yet still called Shirou Emiya by the Big Bad in Drei, then does that mean that Alternate!Kiritsugu adopted them both?
Possibly, in the main series, we never actually know what Shirou's original family was like. So Miyu could very well be Miyu Emiya who survive in the fire along with Shirou. Which would explain why she is so more badass than Illya (Initially at least) and is more used to Combat. Emiyas are always badass. Wonder if she would get her own "Emiya" theme when they meake Dwei into the anime.