As Leif is the GM, his answer is official...I just thought I'd share my personal spin on this question, as it was throwing me for a loop too.
Zoe is of mixed heritage, and favors her Imperial father in looks...most Imperials would not look at her and immediately recognize her as Zhodani. That's one reason she's been 'drafted' as it were, for this duty.
The ship's make and model are Zhodani, but like most things in Traveler, it's been in production for a long time. It's not impossible, or even implausible that such a vessel could have fallen into the hands of an Imperial. Of course, any Imperial engineer who got a look at it would be able to tell this particular ship is of relatively recent manufacture, but the model itself is not a giveaway.
And finally, the original game had us not in Imperial space, but in the Vargr Extents, where Zhodani are more tolerated, in general. The general impression I got was that we'll likely be on fringe worlds and sectors a lot, where weird things like freebooters tooling around in a captured Zhodani ship aren't as weird...or at least aren't as likely to stir official reprisal.
Now, if we strolled into Core with this baby, I'd fully expect to have a flotilla of SDB's barreling down on us right away.
As for tech, I always thought the Zho were just a smidge behind the Imperial state of the art...though I think they're better about distributing their technology throughout their space. In other words, Zhodani worlds have a high -average- tech level than Imperial worlds, but the highest possible Zhodani tech level is a little behind the highest possible Imperial tech level.
Nitpicky little detail though, and unlikely to make a difference. The Imperium is definitely not looking for another Zhodani War, regardless.
Oh, and let me take a stab at that riddle:
Answer: "One, as long as he doesn't die during character generation."