I think most people know the expression, but don't use it very often. A more common expression nowadays might be: Not on your life. Not for all the money in the world.

No, it is an old expression. I have heard previous generations use it, but I never do.

I've never heard that expression, honestly, and i'm 99% sure it isn't used, so, yeah.

I was born and raised in LA but have ever heard the expression "not for all the tea of China" before. But I can definitely understand what you mean by that idiom. Perhaps it is more common in different parts of the US or in other English speaking countries.