There's too much we don't know about the Muses to answer fully.
Let's discuss your thoughts first.
"Anevka", the robot clank that Tarvek's injured sister operated, was a learning machine that adapted to how it was used, and didn't even realize the original Anevka had died at some point during her operation. Tarvek built it himself, based on what he learned from studying the Muse Tinka. Lucrezia also used this same clank, albeit by getting downloaded into an improved head Tarvek had built.
This suggests Muses either can host or can mimic human minds... but doesn't really prove it, given the tech is Tarvek's, "Anevka"'s lack of self-awareness, and Lucrezia's lack of... well, anything resembling humanity. Does make it pretty likely.
Second, we absolutely know that minds - synthetic or organic - can be transferred.
Lucrezia's studies under Castle Heterodyne made concrete that minds could be transferred. Lucrezia was able to transfer the original muse Otilia's clank mind into the organic (mostly) construct Von Pinn, and then transferred the Heterodyne Castle AI mind into Otilia's clank body. Note however, her work isn't without effects, intentional or otherwise. Otilia-in-Von-Pinn's mind was a few fries short of a happy meal by the time of the story, probably not helped by being beholden to Lucrezia's control voice which the Von Pinn body had built in. There's also a really giant question mark about if the Castle AI got forced into Otilia's body, whether or not that was relevant to what the hell happened that wrecked Castle Heterodyne to begin with - which definitely broke whatever mind was left in the Castle.
In addition, we have a hearsay confirmation at a point you haven't read yet -
During the Paris arc, a traitorous Beausoleil (himself a spark driving many clank bodies remotely) states to his (former) master Voltaire, the Master of Paris, that he was only after what Voltaire had learned from Van Rijn, who could move life from flesh to machines and back. This becomes central to the end of that arc - Voltaire has to "become" his city once again, wielding it much like the AI wielded Castle Heterodyne. Colette, Beausoleil, and possibly someone else are also part of the city at points, with Colette becoming Voltaire's successor.
Finally, the Muses themselves.
- Moxana. There seems to be very little point to Moxana's lack of speech. Sure, it forces her metaphoric communication to be more effective, fitting her role. But if Van Rijn's clanks truly were original creations meant to be a pinnacle of form... where exactly did the idea of being mute come from? None of the others were, and the ones we've seen weren't meant to be great orators.
- They did serve the Storm King, but were built to inspire him to greatness, not purely to obey him. ... pretty sure it didn't work. All spoiler at this point.
Also in the Paris arc... a not-so-pretty zombified Andronicus, the Storm King himself, was held at bay in some sort of time stasis field set, kept, and defended by the Muse Prende. Once he's let lose, he's near invincible, 99% mad, and pretty much the worst thing to happen to Paris. Prende does follow him, but at no point does she appear to be under his command.
There are two other Muses, of a sort, other than the original 9. One is the Muse of Vengeance, which appears to have been built by Van Rijn but never activated, for purposes unknown.
The second is the Muse of Time, not actually built by Van Rijn but an apparition he encountered many times in various forms. It's all but confirmed via a memory of Queen Albia of England that the Muse of Time is Lucrezia in various bodies screwing with time travel. Which means the Other War has been going on for a lot longer than anyone realizes. Also... Agatha manages to release the Muse of Time from another trap of Van Rijn's. Notes from Van Rijn indicate he was chasing the Muse of Time for his entire life, but notes from Van Rijn also require some serious sparking to decode every cipher, invisible ink, secret pages, and just plain hideous sneakiness he's built into them. It's not really known whether the Muse of Time inspired the Muses, whether Van Rijn's work is based on Lucrezia's or vice versa, if he gleaned any foreknowledge of the future, or just what the plain hell is going on.