I really enjoyed reading the first couple of chapters. Your characters are three dimensional and engaging, and you put together an interesting crew. But I have to say you switched me off right when you described the Starfleet Cube which is so big it's a little ridiculous. I understand where you're going with it, but I won't be reading more, sorry.
The Starfleet Cube design is interesting because it surprises me. Fleet ship designers have evinced an enduring fidelity to the aesthetics and ethics of their the Federation. Starfleet ships are not painted with dark colours, always that almost white, silvery duranium. Fleet ships almost always have the bridge situated on the top of the ship, flouting obvious danger. Fleet ships--even attack dogs like the Defiant and Akira classes--do not have massive, martially ostentatious weapons arrays. Fleet ships boldly broadcast the Federation/Starfleet ethos of peaceful exploration; sword/phaser sheathed/holstered, but with, as the Capellans say, open hands and open hearts.
I cant wait to see what happens when one of the DQ powers (let's say the Voth) mistakes the Tesseract for a Borg Cube.
The cube is light gray and significantly friendlier looking than a Borg cube. Windows, lights, Federation markings, etc. Within visual range, no one is going to mistake it for Borg. On long range sensors, it's possible. But if you saw something you thought was Borg on your long range sensors, would you intercept, or flee? (Guess that all depends on who you are ...)
One more clarification because I see a couple of people somehow got this idea from the story even though it wasn't stated anywhere ... Irina Marchenko is not the Chief Medical Officer. She is one of a team of Doctors. There is a CMO, but he hasn't been introduced yet.
Still working on rewrites to the next chapters ... more to come!