Arcea Campaign description:
The Terran 1st Fleet, having taken refuge in a mysterious pocket universe at the end of the war of the Dreadlords, have has returned, vowing to cut their its way through across the galaxy and liberate Earth from the Precursor shield that has been it's its salvation - and it's its prison - for the last 10 years.
"Terran 1st Fleet" is a singular noun; therefore, it is appropriate to use a singular verb in the main clause of the sentence, and it is also appropriate to use a singular reflexive pronoun to refer to it after 'vowing.' Changing "their" to "its" is more debatable, as it can be argued that the understood subject of the subordinate clause is the crew of the Terran 1st Fleet rather than the Terran 1st Fleet itself, even though the only noun in the main clause which "their" can refer to is "the Terran 1st Fleet."
Shouldn't Dreadlords be Dread Lords?
It's not possessive if it's not spelled its; rather, it's a contraction of it is.
Arcea Campaign, first mission description:
Hoping to find a safe place to stage their campaign, the Terran 1st Fleet has returned to this universe near the home world of their former ally the Arceans see note. Upon arrival, they discover it occupied by the malevolent Drengin Empire.
Firstly, there needs to be a comma after 'ally.' Secondly, this should either be "their former allies, the Arceans" or "their former ally, the Arcean Empire."
Now they must Liberate Arcea and use it as a beachhead where they can stage their return to Earth.
Why is liberate capitalized? The only words normally capitalized mid-sentence in English are proper nouns; is this for emphasis (if so, I don't feel it's necessary)?
The Vast Drengin empire stands in the way, but they have no idea what is coming for them.
As with liberate Arcea, why is vast capitalized?
The Drengin Empire should probably be capitalized, as this is the proper name of the empire and also for consistency with the earlier usage. As in the campaign description, there's a case to be made that the subordinate clause should read "it has no idea what is coming for it," but there's also an argument to be made that the understood subject of the reflexive pronoun is "the Drengin" rather than "the Drengin Empire."