The movie was freaking great and lived up to my expectations. My only gripe is that they didn't accurately define the factions and their conflicts with each other or I missed it at least.
Are the First Order and the Republic at war?
And is the resistance a group of rebels in First Order controlled planets?
Hey man...sorry about the long post but this should answer your questions if you're interested.
I've read the comics and the major plot points/spoilers from the book "Aftermath" (which is apparently shit), I've also read the wookiepedia and seen the movie twice - this is what I've figured out so far:
SPOILERS BELOW
The First Order seem to have conquered a good portion of the galaxy, or at least intimidated several systems into joining their side, by the time The Force Awakens gets started.
The First Order is either a cult within the Republic that controls it behind the scenes, or an opposing force to the republic within the galaxy.
AFTER ENDOR
To go to the beginnings of the First Order we have to start at the battle of Endor, which saw the Super Star Destroyer Exectuor, which was the capital ship of the Imperial fleet, destroyed. The Imperial fleet lost several admirals AND an important Grand Moff, Grand Moff Jerjerrod, they also lost the Death Star, the Emperor and Vader. So there was, naturally, a leadership crisis in the Empire. Palpatine had intended to rule the empire forever, he had no proper successor and the obvious choices to replace him were all dead. Planets rebelled and some joined the rebel alliance, others claimed independence, etc. That's one of the main reasons the imperial fleet lost at Endor and withdrew from the battle without being able to destroy the rebellion, they lost all their leadership and panicked then withdrew.
The empire reorganized and fought the battle of Jakku, which ended in an imperial rout. The rebellion had rallied enough systems to the cause of restoring the republic that they were able to defeat the imperial fleet outright - the imperial fleet also made lots of bad decisions during the battle and thus suffered their second devastating loss. That was basically the end of the empire. Solo, Luke, et all fought at the battle of Jakku. Jakku is the desert planet where Rey lived. Some small fragments of the Empire remained but the Rebellion seized Coruscant right after Jakku and reorganized the galaxy. They invited planets to join the republic but did not force them to join.
That's possibly where the New Order was apparently able to sneak in and gain some traction. There were certain planets that chose to remain "imperial" in a sense because they had a democratic right to do so. It seems the Republic recognized this as legitimate. So the "Empire" lived on in some places, but they weren't much of a force. The Republic had/has a massive fleet and millions (billions?) of inhabited planets supporting it.
Luke went on to try and re-start the Jedi Knights as the keepers of peace throughout the galaxy but failed to prevent some key students from turning to the Dark Side. I guess a major risk associated with teaching people about The Force is that people are flawed and might be turned to selfishness and rage for any number of reasons.
Luke taught some kids some lessons, and badda-bing badda-boom, he lost control of certain students. This "supreme leader Snoke" who may or may not have been a student of Luke's started a cult and recruited members, he managed to brainwash Ben who becomes Kylo Ren with stories of his grandfather and promises of power, and any number of other cult-esque strategies that tear people from their families.
ENTER THE FIRST ORDER
This cult gets in contact with whatever remains of the Empire and they form an "Alliance to restore The Empire" kind of thing, and either go on a warpath starting a full on Galactic war, or, they operate as a cult/independent territory and via cold war tactics they terrorize the Republic; OR they operate as a behind the scenes cult with a smattering of forces around the galaxy - it's not clear what was going on politically in "The Force Awakens" (probably by design since Disney knew Abarams only had 1 film on contract and they didn't want him designing the entire new universe).
"The Resistance" seems to have been formed within First Order territory, or, as an offshoot of the Republic that would not sit idly by and watch the Empire re-form under the guise of --whatever it is-- that the First Order did to take control of systems.
WHAT THE HELL IS GOING ON?
As of The Force Awakens, the First Order is either:
A) In a full on war against the Republic, but they fear to engage the Republic fleet outright and the Republic Fleet is also unwilling to engage in a decisive battle, so there's a stalemate
B) In a Cold War against the Republic, where they engage in occasional skirmishes that see various territories ceded between one party and the other, followed by peace treaties.
C) Is a cult that is controlling the Republic behind the scenes and can't be crushed because of corruption
Whatever the case may be, the First Order is also fighting a resistance within the places they directly control that is supported by at least some elements of the New Republic, based on the lines of dialogue we heard in the movie.
Hope someone reads all that someday...
