According to [1], in Japan, 4.5M people play Mahjong (in Japan you can assume Mahjong means Riichi Mahjong), 5M people play Shogi, and only 1.5M play Go.
Interestingly 21M (!) people play family games, which means party video games, e.g. Mario Kart.
I don't know for riichi mahjong, but "mahjong" is pretty popular, yes. But the betting aspect puts it probably closer to poker than chess or other games where money is rarely involved.
At least in my circles it is common that people play or have played, especially males. I myself play on average two tables or so per day online. Although I certainly should force myself to read up a bit more on strategy.
Not exactly. "riichi" comes from Mandarin, which might be related to "reach"[1] (can someone confirm?). It is an original word, although maybe a loan word, an the pronunciation might just have been kept faithful to the original because for all three languages (English, Chinese, Japanese) the length of vowels are sometimes meaningful (unlike e.g. in French).