Battlefield 3/WMG

This "PLR" that you're fighting against in BF3 is not some radical Arab jihadist group...
..They're Kurds. Here's my evidence:
 * The first level takes place in Sulaymaniyah, a Kurdish city in Northern Iraq.
 * The name "Peoples Liberation and Resistance" doesn't really sound like a jihadist organization. If it was, they would use terms like "Islamic" or "Mujihadeen", or such. The PLR is probably a splinter or successor organization to the PKK.

Here's how it went down. Back in 2003, the United States invaded Iraq and deposed Saddam Hussein. The Kurds had long been oppressed by Saddam's regime, who had used chemical weapons in an attempt to exterminate them. The Kurds were initially grateful to the Americans after having been liberated. But the Kurds, being the largest ethnic group in the Middle East without a country, wanted to establish one. However, America put a stop to it, fearing that Kurdish independence would destabilize the region and that other stateless ethnic groups (Such as the Palestinians, Baloch in Pakistan, et cetera..), would also would also want to be independent. This, along with the continued presence of U.S forces in their homeland (the game takes place in 2014, and by then the U.S military might be wearing out it's welcome), enraged the Kurdish populace. In response the PLR was formed, which began attacking U.S marines, leading to the events of the game.
 * The revelation in the game and novel that the PLR originated in Iran would seem to put paid to this particular theory. Though the part of them not being an Arab jihadist group proved correct; they're decidedly not Arab, and their aim seems to be more along the lines of secular Iranian nationalism Gone Horribly Wrong.

BF3 is not only a sequel to BF2, but BF:BC2

 * The squad from B-Company will show up as major characters halfway through the game, and they will kick ass a-plenty.
 * Previous pre-release materials have specifically said that that would not be the case...but hey, there's always Lying Creator. I can't deny that seeing what you said would be absolutely awesome.
 * Nope! DICE has stated multiple times that BF3 is a direct sequel to BF 2, which in turn is a sequel to BF 1942. The Bad Companies are set in an entirely different universe, albeit one which is quite similar to the one already established.
 * And besides all that, a recent interview stated that a proper sequel to Bad Company 2 might be in the works for the future, so there'd be little point in cramming any related material into BF3 (not that it works much better in its intended role as a BF 2 sequel; where the heck did China and the MEC go, and when did Russia get involved?).

The PLR arose from the 2011 Iranian protests.
Exactly as it says; a faction of protesters got a little carried away and formed a radical organisation that, by 2014, was able to violently seize control of Iran, and proceeded to use it as a staging area to launch PLR attacks in Iraq and other regions. As for why I'm going with Iran as its source rather than Iraq, I'm going on how the wiki mentions a new President of Iran who took control in a coup and has ties to the PLR, and a quote from a character in the tie-in novel who says, "Better learn Farsi," in relation to the idea of the PLR taking over. The game itself suggests that they've been making trouble in Iran for some time by 2014, with the earthquake at the end of the first mission being the last straw for Iran's beleaguered government, allowing the PLR to take complete control.

The Rat was specifically trained to seek out US soldiers
IRL there are people who have been training rats to do mine detection, it's not that far a stretch to think that rat may be trained for search and rescue ops, even without electronic guidance. So the PLR got their hands on a few S&R rats, released them on the earth quake zone and had a soldier follow them with an assault rifle. Hilarity Ensues.

Battlefield 3 is a prequel to the Bad Company games.
The singleplayer campaign explains how and why the rather unclear Russian-American war from the BC games got started, and the multiplayer depicts some of the earliest engagements.
 * Yeah, that's outright immpossible. Considering that BC took place in the Vietnam War, and BF3 takes place in 2014. Who knows, maybe they have a time machine!
 * What are you talking about? Bad Company takes place during the modern era. Did you not notice the Blackhawks, the Humvees, the M 1 A 2 s, the soldiers' armor, and the guns?
 * Yes, that's absolutely impossible. The Bad Companies take place around 2010, and BF3 happens in 2014. Also, in the Bad Companies, the fighting is mainly restricted to Eastern Europe and South America, rather than Iran. Also, there are references that the war in BC is a war over oil, and the one in BF3 is over nukes.
 * If anything, the BC games are prequels to BF 2142.