Jiu is nine, Shi is Ten. When you're putting it together it's like 9 x 10 yuan so it becomes 90 yuan (First Rule). But, there's an exceptional if you put Shi(Ten) before Jiu(Nine) it equals to 10 + 9 yuan = 19 yuan (Second Rule). Ten, One Hundred, One thousand will follow the second rule while other numbers will follow the first rule. Keep Learning folks!
1，000，000=一百万 hence 百万富翁=millionare (富翁=rich man)
Note that two can be 二、两、俩(used more in the sense of two people, e.g. 我们俩=the two of us, 哥妹俩=the (two) brother and sister)
Good question. I thinks I see your point here. Depending on which mothertongue you are coming from it might help to think of it more as yu-an.
The yu can be pronounced like the y in "yes"+ the French u or German ü. Sometimes the y can sound more like the g in "gibberish". Try saying it loud and compare it to the recording. The second part is imho quite close to the English "an" and from what I've read that appears to not be your mayor problem.
Be careful to not confuse Yuan with Yen.
Yen or 円 is the basic monetary unit of Japan; which is actually said as "En" rather than "Yen". Yuán or 元 is the symbol of a currency unit (Chinese Yuan). For money, cash, dollar, etc, you'll likely see a few other characters 美元, 钱, 金钱, 货币, and possibly others. You'd have to research to see what is used, how often, and where(geographically).
"九十元" = "Ninety yuan." The reason there is a "十" is based on Ninety's (90) second digit. one digits are 1, 2, 3, 4..then second digits 10, 20, 30, 40. english doesn't pronounce 2 as 'twenty', so that's one thing to keep in mind. Yuan is the chinese currency. it's weird how they do not show the definition of the currency so you won't have that question, but now you know.