Fate/kaleid liner Prisma Illya/WMG

Sudden drops in magic power are partially because of Zeltrech's Gem Sword
From time to time, characters comment on how a magical attack isn't nearly as strong as it was a few panels ago. This is because Zeltrech's Gem Sword, which drains Mana from its alternates in other universes is doing its thing in Another Dimension. Kaleido Ruby and Kaleido Sapphire being components, and having no problems at all firing gobs and gobs of Mana are prime targets.

The series is set after a successful Holy Grail War
One where Ilya got her wish. In the Ilya route in which this occurs, the only survivors were Shirou and Ilya herself; Ilya, wishing them both to be happy, created a new universe where everybody didn't have horrible backstories, and all the dead people, well, weren't dead. The new universe contained many of the concepts of the old, in new forms. In the process, she sealed away both her and Shirou's memories, and entrusted their guardianship to her creepy maids.
 * Which means basically that the Grail Conduit wished for the power to keep existing; thus Ilya retains a connection to the Akasha. Normally the Wish would be able to handle this; but the rule-breaking aspects of the Kaleidostick are massively screwing with this.
 * The Corruption of Angra Manyu had to be sealed away into the Cards.
 * So very close. It's . Of course, this reality could have been created through Time Travel via the above theory.

She came from the future where Illya is able to fully utilize the She also came to love Miyu, thus her lack of embarrassment from kissing Miyu to drain her mana, possibly enjoying it.
 * She obviously also still has a thing for Shirou.

is actually the Ilya from the doujin Sword Dancers
I mean, look at the resemblance!

Heroic Spirit EMIYA will show up
Because this storyline needs more GAR.

Ilya and Shirou's parents are looking for a cure for Ilya
Related to the "sealed power" within her, that's why they're gone all the time.
 * I Knew It.

Miyu is a magical copy of Shirou's biological sister and Homunculi
After Kaleidoscope Ruby sought out Ilya; Luvia Edelfelt realized that Kaleidoscope Sapphire was going to do the same thing. Instead of just finding out who it picked and bullying them; she got a little proactive. She created a being with the aspects that Sapphire would most be attracted to; and programmed her to obey her. The person she based the Homunculus on was randomly one of the people who died in the fire that made Shirou an orphan. When she realized just who she copied; she told Miyu not to tell Shirou. Shirou has amnesia of his life before the fire; and this was the age his sister was when she died.
 * Black Ilya does tell Miyu that her existence is similar to her own; born of magic.
 * Of course, this means her lifespan should be very short; but chances are this series will find a way to fix that.

Ilya was the vessel for the Fourth Grail War.
For some reason, the souls of the defeated servants was transferred to Ilya instead of Irie, and she become the vessel. Thankfully, Kiritsugu managed to kill Kotomine after the great fire, win the war and had the Mage Association save the barely alive Ilya and dismantle the Grail. Unfortunately, remnants of the grail and its corruption still reside in Ilya, so her parents search for a permanent solution across the world, leaving her under the care of her Homonculi maids and a survivor of the great fire that they had just adopted.
 * Possibly confirmed.

Black Ilya is the same Ilya Archer knew during his life time.
We know that Ilya died a year after the war in Archer's time, but perhaps Shirou tried to save her life by transffering some his power to her. This caused her to begin exhibiting powerful projection abilities and her skin turned darker (like what later happened to EMIYA). At some time before she died she used these abilities to do something incredibly badass that ended up netting her a place in the Throne of Heroes until she some how got dragged into this reality. This of course means that if Heroic Spirit Emiya shows up later in accordance with the above we can be expecting a a very touching reunion.

Sakura will play a role in the third story-arc.
Sakura will show up as a Dark Magical Girl rival to the heroes a la Fate Testarossa, and she will have her shadow powers and obscene healing factor. She will eventually get "befriended" by Illya, will become a permananent resident of Shirou's harem, and the people who manipulated and tortured her into doing what she did will get their comeuppance. A possible Kaleid Liner Prism Illya 3rei! in a nutshell.
 * And Counter Guardian EMIYA shows up as well, to make the story even more badass.
 * Well, Sakura indeed has appeared in an Omake, but we'll have to see if she's only a one-chapter character or will become an recurring character.

Matou Zouken created the cards.
In the classic Fate timeline, he is the one that created all of the servant-binding spells, including the class system. So it makes sense that he made the class cards in this one. This could be relevant if combined with the above theory, as Matou Sakura might be able to use the cards in some special twisted way.