Doesn't akahadaka mean nakedness?
Green is very, very often associated with nature. "Green Day" is Japan's Earth Day. One word for "baby" is akanbou, which basically means "red boy." A word for "youth" is "seishun," which is literally "blue spring [the season]."
I'm not surea bout "red carpet," but in SpaceALC's long list of examples of English's "red carpet" phrase, they all seem to use something like 盛大な歓迎をする (to give a grand reception). I saw one talk about 赤いじゅうたん, which is literally "red carpet." However, this example was literally talking about a red carpet being rolled out. My best guess as a non-native is that it is not used metaphorically in Japanese. You can only use it in the literal sense of "there is a red carpet there" or "the servant rolled out a red carpet." You do not mention a red carpet when using it in the metaphorical sense of a "red-carpet welcome."
“red carpet”の検索結果（24 件）：英辞郎 on the Web：スペースアルク
I wouldn't say blue is a sign of only either lying or loyalty in "European languages." For example, in English (definitely a European language), "blue" connotes sadness, but it also connotes loyalty (true blue), aristocracy (blue blood), etc.
I'm pretty sure purple is thought of as royal in Europe. Kings in medieval Europe wore royal purple, which is similar to the royal blue worn by the aristocracy.
Purple - Wikipedia, the free encyclopedia This webpage on color psychology states that purple is the color of royalty
Color Psychology not blue.
However, some of what you're asking is more psychology than linguistic. I daren't suggest the psychological answers since I'm not from Japan. I did, however, offer historical and linguistic points of interest for you.