Sorry this took such a while - hope you haven't been holding your breath

. And this is just chapter 1

...
Or as you like to call it, fate.
Technically, there should be a comma after 'Or'. 'as you like to call it' is a clause that just adds extra information - the sentance would still make sense without it. So, it must be surrounded by commas.
The arrow of time may guide our way onwards through the dark, it does not take away your responsibility towards the universe.
Comma splice there - you're joining two complete sentences with a comma. Either change it to a semicolon, or add 'and' or 'but' after the comma. Of course, you can leave it like this - comma splices can be a matter of style. I'm just making sure you know.
That too is entropy.
Again, 'too' should be inside commas.
It soothed her mind, calmed her thoughts.
This is another comma splice, but you can leave it for stylistic reasons. I would leave this one if I were you, actually. Meh.
Here the three stars Alnitak, Anilam and Mintaka have captured people’s imagination for ages.
Seems like a little tense confusion. You're writing the narrative in past tense, but here you switch to the present. I understand why, but I think you usually remain in the past - so in this case, 'have' should change to 'had'.
Only a few light years away from her current position, it was the star that had given the space around her its name; the since the year 2583 populated Zeta Orionis system.
'the since year 2583 populated...' sounds really awkward. Maybe consider 'the Zeta Orionis system, populated since the year 2583.'
And that was why the Terran Covenant had constructed a Golem II research station here two and a half years ago; to observe the creation of new suns in the nebula complex.
That semicolon there is a little out of place. For a start, the 'to observe...' clause isn't a complete sentance, so you can't legally use the semicolon to add it on - you need a colon or (I think) comma. Stylistically, a colon works better anyway, so that's my recommendation.
Arya had not been assigned here to ask questions though.
This is another one of those places that needs a comma - and this one really does need one, right after questions.
If only she could shake that uncomfortable feeling of suspiciousness constantly recurring in the back of her head.
I was about to tell you that suspiciousness isn't a word, but blow me down and pick me up, it is. Huh. Must be an American invention

. Anyway, this sentence is grammatically perfect, so do not feel obligated to change anything at all. But if I were you, I would have written 'suspicion'.
It boasted eight fast-tracking heavy argon ion lasers, or HAIL’s for short, and a small complement of missiles.
No apostrophe for the plural on HAILs.
She could know, since it had been the Solarion’s turn yesterday.
Technically speaking, this sentance is correct. However, the usual expression is 'She
would know', which is what I think you were looking for.
“Tactical, charge weapons and line up the HAIL’s with the convoy’s approach vector,”
Apostrophe in HAILs again.
As to affirm that statement, the com crackled:
Again, grammatically I think there's no problem here, but we usually say 'as
if to...'
They can be here any second now!
Usually, it's 'They
could be here...'
The beam caused the still unused deuterium fuel to fuse on the spot, exerting an enormous amount of heat and pressure on the already heavily damaged reactor.
Bit of a curveball here. The 'still unused deuterium fuel' is a bit ambiguous - is the unused fuel still (like Lake Placid) or is the deuterium fuel still unused. Now, if's obvious what you're meant to mean, but the ambiguity could be alleviated by hyphenating still-unused. Not strictly necessary, but meh.
Where the salvo’s of sapphire blue energy hit the hull of an F-214, the armour plating disintegrated in bright flashes of light.
Apostrophe for plural in salvos.
Those xeno’s are going to pay dearly for what they’ve done.”
Apostrophe for plural in xenos.
“They’re to fast, sir,”
Should be 'They're
too fast...'
are they, some kind of new Ayani Yakuza ships??
This is another thing that's stylistic, or just personal preference. I refrain from ever putting double punctuation marks, no matter how much it adds to the emphasis. It's not technically correct, I don't think, but I know some people do it.
Dear Lord, what are these things?!
Same again. I would remove the exclamation mark.
Arya thought bewildered.
There should be a comma after thought - bewildered is extra information.
“With all due respect, but what in God’s name could you possibly do to stop these monsters?!”
In the first part, the 'but' is superfluous - it is used to join two complete sentances, but these aren't complete sentances you're joining.
And there's the double punctuation again

.
Arya feebly tried once more, knowing in her heart how this all would end.
'this all would end' sounds a bit archaic - usually you just say 'all this would end'.
He knew he had to be brief; the xeno’s could hack the secured link to the Solarion any time now.
Apostrophe for plural in xenos.
Arya could here the captain of the Galinor almost laugh about his own morbid sense of irony, right before he spoke his final words:
'Arya could almost
hear'
Again, there's a little ambuguity after that - 'almost laugh'. Do you mean she could almost hear him laugh, or she could hear him not laughing, but almost laughing? If the former, then 'she could almost hear him laughing' would be better.
The pilots at the dual helm, two young men in their late twenties focussed on the job at hand; one of them already plotting their escape vector while the other turned the helm hard to starboard.
The semicolon here isn't joining two complete sentences - if you took away the first one, 'one of them already plotting their escape vector while...' isn't a complete sentance. I reccomend adding a was: '...one of them was already plotting...'
As soon as the frigate had turned half-circle, the engines engaged at full power.
Word missing - '...had turned
a half-circle...'
Then the fusion reactor onboard the Galinor self-destructed, turning the ship into a miniature supernova and consuming the still firing xeno ship in the immense expanding fireball.
Ambuguity again - was the xenos ship still, or was it still firing? If the latter, hyphenate still-firing.
The status display in her captain’s chair now had icons flashing red uninterrupted as the engines were systematically being shot to pieces.
'uninterrupted' here is an adjective, but it's describing the way the icons flashed - so it should be an adverb, 'uninterruptedly'. Though stylistically, I would go for 'icons flashing uninterrupted red'.
“What the hell is happening?!”
Same old, same old...
I'm really just bringing these to your attention - whether you change all of them, some of them or none of them is totally your decision.
All communications are down and both the hyperspace beacon-locator and transmitter are fried.”
'transmitter' should be plural, since you refer to 'both of them'.
Research Station 128 has been reduced to Swiss cheese; cauterized big holes through-and-through caused by an unknown energy weapon cover the entire station.
This is another issue that's a bit pear-shaped - 'cauterized big holes'. I can't really explain it, but 'big cauterized hles' seems more correct. Maybe it's like french - certain adjectives have to go before or after the noun. But in this case, it's just the order the adjectives some in.
It is in a similar state as RS 128; being littered with impact holes caused by an unknown energy weapon.
That should be 'in a similar state
to RS 128'.
About the whereabouts of this ship can only be guessed, and I find the only possibility forwarded by my own logical circuits - that the Solarion is lost in hyperspace - unsatisfactory.
The 'About' here is unnecessary, and I suspect it's just a holdover from being written in Dutch.