It is regarding manipulation of magic circuits, storage of mana and also help her unclog and align her own magic circuits

Due to story relevant things, Alesh is a 2nd rate mage due to her own body being a mess. Even when she has the aboundance of Mana flowing and providing for servants without a holy grail

That is a what if story with Alesh.
It is a bit of a spoiler of the story. But Alesh did try the summoning a servant before Kagetora 1 year earlier, but it was deemed as a failure for her as nothing seemed to happen.

For Alesh it was a matter of chance. Her goal was to get one of the North European heroes specially a Caster for her own mage experiments.

Due to circumstances she is incompatible with 99.99% servants.
Kagetora was that anomaly, the 0,01% that would and could answer Alesh's call.

It has something to do with her magic yes. I hinted it at the - Grudges part 2 page.
While I don't want to go too much into details. Alesh have a way of purifying evil spirits but it does comes with a cost of having to use her own body as a medium after she used her magic.

One can think of like how the liver in a human detox things. Just that Alesh uses her whole body for it.

That is a question which is hard to answer.
Kiyohime is to begin with 14 years old while Astraea is a god and very old. This would mean that they prob not be a couple but good friends that is a possibility.

Astraea and Eresh are both godesses of different domains and while the are using vessels of Luvia and Rin that had a rivalty. there is still a possbility for them to be friends. That is ofc if they aren't summoned as enemies.

It is actually not a grail war at all. The summoning of Kagetora is the biggest hint so far.

What i can say is that a lot of this is remnants of former grail wars accumulated to a boiling point

Alesh is an adopted daughter of the Askar family that had gotten the task to take care of her. The family is in the Scandinavian area.
She got the basic education of magic from the family and was later sent to the Clock Tower in Britain that takes over the task of taking care of her.