This is unrelated to the film in any way, its referring to the people that designed the animal characters that are based on the characters. They are referring to the goods designers for the goods depicted here. By the way, just to add in, the products are called Dōbutsu K, literally Animal K.
The Sword of Damocles is the direct manifestation of the Kings' powers and their state as a King. If they were to lose control of their powers due to personal emotions like Mikoto's rage of Tatara's death, the swords start crumbling. This is due to his Weismann levels raising as his compatibility as the Red King is falling. A similar thing is happening to ...
There are two possibilities for what the "K" refers to.
The first is Adolf K. Weismann, who is the original person that became Yashiro Isana, the main character of the show.
The second is "King". The leader of each clan is its King, who controls the members of the clan. Weismann is a King.
KINGS is also the first opening theme of the show.
If you mean publication order, the K wikipedia article's manga section doesn't list all the publication dates, but seems to list them in publication order.
By serialization publication start date (end date included if applicable/known):
2012 ? (no later than November) - 2013 ? (tankobon release 2013 April): K Stray Dog Story
2012 May - 2013 July: K -Memory ...
This doesn't answer your broader question, but the K: Return of Kings soundtrack is scheduled for release on April 27, 2016.
Are the soundtracks always released?
Not always, but I'd guesstimate that 80-90% of anime have soundtracks released at some point. Those that don't are mostly shows targeted at children, who are probably not likely to buy ...
You should watch the movie, as it is related to the storyline of Return of The Kings (ROTK). If you don't, you will not know the major changes that have been made, nor the main villain of ROTK, nor will you know what happened to Shiro. These were all revealed in the movie. They would just allow Shiro to show up and you would not know what happened to him or ...
He willingly put himself in that position to have a private dialogue with the Blue King about the whereabouts of the gray king who killed his clan-mate.
Since they are Kings and of opposite factions they couldn't just sit down and chat without a fight. Suoh was also in major danger of causing a Damocles Down event due the deterioration of his sword.
HOMRA (吠舞羅, homura). It's not 炎, the spelling is different.
The Arabic word "حمرة" which means "redness" must be the origin, it is the red clan after all, and the spelling is identical. (try the speaker button on Google Translate for the pronunciation)
In season 2 episode 3, Kismet is from an Arabic origin as well.
From the first to last clans, they are White Rice Party, Tokijikuin, Homra, Scepter 4, Jungle, Cathedral, and Colorless. Cathedral was COMPLETELY destroyed in the kagutsu crater incident, therefore the only one in the series that has any resemblance to the powers of the Gray clan, is the Gray King Seigo Ootori. (Tenkei Iwafune) And any sort of information ...