Some more questions and a few observations that may be useful.
First, how big was the Empire? Whole galaxy? More than half? About half? Less than half? Less than a quarter? Smaller still?
This largely defines how good your FTL and Comms are (or you can go the other way and use those values to define how big the empire was). As other people have noted if comms times start getting large then you need to operate the provinces as largely independent holdings (quite probably with significant military and manufacturing resources) as help from the core could take a very long time to get there. Certainly this type of arrangement lends itself to severe fragmentation after the empire collapsed. I'd assume one to two months at most from the Capital to provincial capitals and maybe another two to three from the provincial capitals to the periphery from the sound FTL description (probably a X-Boat network for comms). Are travel times consistent for the same distance everywhere? Is it possible two ships to spend a month in transit yet cover different distances based on the start and end points of the trip?
If transit seems instant to the crews on board, then there is potential for there to be at least a few old Imperial task forces wandering around still in the far reaches of the devestated areas that are not yet aware of the new political arrangements (or even that the enemy has been defeated/driven off). Will they go rogue? Declare for the Emporer? side with a province? Setup their own province (this is less likely unless they can solve their logistics issues independently)?
If you want FTL comms then perhaps a leaf out of Starwars may be useful - almost all ships had FTL comms, but limited to 20 or 30 light years (say about 8 parsecs if you prefer) at most. Longer ranged comms were possible, but required huge installations with massive power (planets and largert star destoyers only). Relaying smaller unit together for comms would also be possible, but not as fast and there would be extra security issues that might make it unsuitable for military comms.
How many of the thirteen provinces are still more or less functioning as entities? I'd assume that since the Capital was devestated, that at least one and more likely three provinces were smashed (maybe more) and at least parts of other were damaged (unless of course the Aracene had enough technical advantage, material and logistics capacity to invade from multiple locations - in which case how did they lose?). How are the provinces arranged? Spokes on a wheel style? Concentric rings, with each ring broken down into sections? An emporer implies a certain level of direct control over each province so each provincial capital is likely to be more or less the same travel time from the capital
The Emporer would have fled the Capital prior to it's destruction, but from the sound of it while he controls a portion space nearby to his new Capital, his ability to project power may be severely limited. Until he can construct more ships that is (and obtain and train personnel for them), but then he needs material to build them with which he cannot readily obtain..... Cue agreements, under-the-table dealings, smuggling, "tribute" missions and whatever else. Do not forget to factor in the level of delusion the current Emporer may have as well. Does this person have an accurate grip on the situation or are they operating under the impression they have more influence than they really do? Are they merely a figurehead for someone/something else. Certainly the defences are being run competently and the troops are still well trained, so something is going right. Power projection though....
From the sound of it the Magistrate (is it *really* the magistrate?) has managed to reproduce some group of alien technologies (it's wildly unlikley to be just one tech in isolation) and has managed to use them mass produce this one particular innovation. What other innovations are being worked on that cannot yet be mass produced? The description implies that he is operating out of one of the devestated areas, so it's likely he is constrained logistically from doing too many things production-wise simultaneously. The questions on eveyones minds are likely to centre around how much of the success the magistrate has had are down to technical superiority? Good Logistics/Strategy/Tactics/luck? Poor opposition? Cue much spying, speculation and the occasional military probe? Let's not forget the traitor in his ranks either...
The Parliament - a semi-toothless tiger strung together by the surviving provinces. The only reason they have even a semi-effective military is because everyone else would be at least somewhat paranoid about the Aracene returning (plus the magistrate, plus the Emporer) and of course what better way to get one of your ships with your spies into someone elses territory legitimately. However with a core command group that is more or less free of other ties it may yet turn out to be the only group capable of withstanding the other forces in play and maybe even grow into something better.
The provinces - Those few that survived largely intact will likely be the current economic power houses in the current scheme of things. The other breakaway groups or smaller provinces that haven't been absorbed will be treating them like the 800lb political and economic gorillas they are. They are probably wary of each other to differing degrees and playing diplomatic and/or military games with the smaller players as suits their current rulers temperaments. Cue much spying of course. Depending on what their fleets are like there is probably a fair bit of piracy and things like letters of marque may well be in play. Mercenaries and "independent naval operators" are also likely to be popular. The partially damaged provinces are likely to be military and diplomatic hotspots as the larger provinces try to gain control of their resources and they try to recover the devestated areas - unfortunately for them populations only grow so fast and recovering a lost colony isnt cheap (though less expensive than establishing a completely new one).
The periphery - Anything goes out here. The major navies are likely to be focussed on more internal issues than out here, but they might have bases secret or otherwise and depending on how much attention they pay to things this far out. even very large events may go unnoticed.
Well that's my current brain dump. Hopefully these questions get the thoughts flowing.