Professor Q is basically Flash + Green Lantern + Reed Richards' intellect. The OP picture is a good indicator of all of those things. The fact that she appeared in ridiculously few comics is the only thing keeping her out of the "Is she Skyfather+?" KMC sweepstakes.
Match her against heralds and we start to have to say "We don't know for sure" simply out of deference to her limited showings. But someone like Iron Man is clearly outmatched.
I was going to say something similar to Digi. She has barely any appearances, but going by the hype she is definitely up there. That could actually be said for a few of The Monarchy characters.
I really don't know. She doesn't have enough showings to have defined limits. We'd be guessing at about anything from Mid-herald to Skyfather+/Low Abstract. My guess is that she falls somewhere in the trans. department, but I'm hardly assured of that.
My memory is very vague here. I recall her pulling all of her power from a supercomputer in the future or some such, that was either powered by or literally was a star. The bio you linked references a connection to a future computer as well.
Either way, all tech in the universe? I don't think that's the case. But she is a genius-level intellect with access to some formidable future tech, at the very least.
The bio Prep linked says that she was thought to be tapping into the computer system of the future version of Spartan--the Godlike version Majestic battled at the end of time. Is there any truth at all to that?
I don't remember, sorry. I don't have any recollection of the Spartan-computer, but that doesn't mean it's not there (I think I read the Monarchy before anything with his future self in it, so maybe I just didn't recognize it at the time)