Doctor Carmilla

Doctor Carmilla (played by Maki Yamazaki) is the creator of the Mechanisms.

The Siren Saga
Doctor Carmilla's original home, the planet Terra, was destroyed and is now uninhabitable. (Specifically, it mentioned that they were gassed, in what might have been a war of some kind. ) It's also mentioned in an introduction of her music that it could be an alternate universe in which World War II ended differently. During these events, Carmilla lost an eye.

Carmilla was with her lover, Loreli, while this happened. Loreli seemingly died of some sort of disease but came back to life. Extrapolating from this, it's fairly likely (but not canon) that Loreli was the other of the only two vampires that exist in the Mechanisms universe. After this, Loreli seemed changed in some fashion, to the point of hurting Carmilla. Despite how toxic their relationship became, Carmilla was still in love with her.

However, at some point, Carmilla struck out on her own and ended up forming the Mechanisms, so something most likely happened between them.

With The Mechanisms
Carmilla created all the Mechanisms (with the exception of Marius and Raphaella) and traveled with them on the Aurora for quite a while. It's likely that the song Eleven references King Cole's war (from the album Once Upon A Time (In Space),) which would mean she was present for it. She permanently left the Mechanisms soon before the events of Once Upon A Time (In Space). The Mechanisms believe that it was because she was pushed out an airlock by Jonny D'Ville, but she didn't actually leave via the airlock. (Not much more is known about this.) However, there were several failed attempts at pushing her out of an airlock beforehand.

After the Mechanisms
Carmilla found another ship called the Silvana, and spent time on that in something called the Weird. (Edit from someone who knows more than me about this would be helpful here.) She attempted to clone herself, which led to the in-universe version of Maki Yamazaki, who is canonically a failed clone of Dr Carmilla. This may have been related to the larger process the Mechanisms were apparently a byproduct of.

She is forming a new band. However, the members are not Mechanisms.

The Mechanisms
She views all the Mechanisms as her kids (including the Toy Soldier, which she didn't mechanize), and says that she loves them. However, their relationship overall is very negative, with Jonny being visibly scared of her and mentioning her killing them like a common thing. Nastya also seems uncomfortable, especially when Carmilla touches her. The other Carmilla-era mechanisms seem more calm around her than those two, but only slightly.

Aurora
Carmilla raised the Aurora from a young age, and seems to like her quite a bit, maybe even slightly more than the other Mechanisms. (This probably doesn't mean that her relationship with Aurora is positive, though).

Trivia

 * She is fluent in Japanese.
 * She has the same kind of healing factor as the Mechanisms, which enables her to come back to life.
 * Vampires can apparently get drunk.
 * The Silvana has a bad Wi-Fi connection.
 * Her blood type is apparently 'V+'