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.
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).