vagueGM says:
For those of us not all that familiar with SW dates, I assume that '2 months prior to the Battle of Yavin' is shortly before the original movie? Right?
Is there anything significant happening at this time that we should be aware of?
Yes, two months before the destruction of Alderaan at the hands of the first Death Star and then the destruction of the first Death Star in the vicinity of Yavin 4. (basically the galactic events of Episode 4...or as the called it in 1977...STAR WARS) :)
My hope is to tie the events of this story into some of the things that will be happening in Episode IV and beyond, but to answer your question about significance, the Empire is continuing to expand. I think by the end of Chapter Three (as I foresee it), there will be a definite nod to events in Episode IV.
For now, star systems all the way in the Outer Rim at this point are falling under Imperial Control. Depending on where you're at, life may have not changed much (corrupt Republic officials replaced by corrupt Imperial officials), or its gotten better as some Imperial Moffs, similarly to the Romans in antiquity spoke to the rulers of planets and systems and explained that they can join the winning team and enjoy all of the benefits of Imperial knowledge, technology, and that the galactic Emperor was not going to take no for an answer...so, make the best of it and maintain order and peace with all the benefits of the Empire. This greatly benefits people who need and want the basics, like jobs, food, shelter, etc. There are still planets that have been completely devastated by the events of the Clone Wars. The Empire helped clean up some of the those worlds, and continues to do so. On the other hand, people in systems governed by people like the "Rule by fear, Display of power" mentality like Tarkin, have no voice and get a boot or blaster bolt to the head if they dare speak up.
We're in a time that's right on the cusp of moving forward.
There's an event in Episode IV that is briefly mentioned but has great consequences for all Imperial subjects, especially for those who end up getting a boot or blaster bolt to the head if they try to go against the grain. Moff Tarkin mentions that "the Imperial Senate will no longer be of any concern to us. I've just been given word that the Emperor has dissolved the council permanently. The last remnants of the Old Republic have been swept away."
Uh oh. No more pesky representatives of the people to give advise to the Emperor on how to conduct business. That was a huge development! The Emperor at the point at where you're at it in the timeline is slowly getting fed up with the bureaucracy and law makers interfering with his plans, so eventually, he gets rid of them and Tarkin further explains to shocked Imperial officers that the regional governors will maintain control (these are Palpatine's hand picked people).
That's the time you're all heading into, and there's quite a bit of tension between people trying to figure out whether the Empire is bad, good, a little of both kind of like the Republic, and of course, depending on where you're sitting things can already be pretty bad (ask the Wookiees and various other races that have been enslaved or have Imperial garrisons interfering in local law enforcement, politics, etc), or it can be quite good (there are peoples who were helped by the Empire either because the Empire saw a benefit or there were benevolent Imperials helping people who needed it).
Once Episode IV rolls around, people will sour on the Empire and tensions get worse (even some Imperials will sour on the Empire), but the Rebellion will unify which it hasn't done so yet in the times you're starting out in (per the events of Rogue One, they were disjointed as all heck).