Just a pedantic comment, but 有り難う is arigatou or roughly "thanks", not "hello". Hello would usually be こんにちは or, more confusingly, 今日は
I don't know how to type japanese on my phone, but the first is literally "early" surrounded by honorifics. The characters for konnichiwa means "this/now", "day" and the "wa" at the end is an article making the previous phrase the subject of the sentence. Same with konbanwa, but for evening instead of day.
no idea on the etymology of moshimoshi for answering the phone, though.