Limassol has gained no traction? It's right on the spot on the map, is Cyprus's #2 city and is politically important due to a sovereign U.K. base on an island nation in a proxy battle between Greece and Turkey, both NATO members.
Los Angeles translates as The Angels, as in "Our Lady the Queen of the Angels of Porciuncula" ("Nuestra Señora La Reina de los Angeles de Porciuncula"). If you're worried about a grammatically correct shorthand being used, the definite article is the least problematic. You'd better stump for Señora, Reina or Porciuncula. I wish you luck.
I don't think so. Larnaca is the oldest city in Cyprus. It's also home to the country's only major airport, and some popular beaches. Limassol is larger, and also where the major seaport of the south is, but I don't think it's "much more well known" than Larnaca.
I don't know. I know the existence of Limassol for twenty years, and this quiz was the first time I ever saw the word "Larnaca". More significantly, the wikipedia page for Limassol is much longer (at least in English and in French).