I'm not entirely sure what you mean by "pure economics", and you're asking two different questions here. One asks about economic theory; the other asks about issues that would definitely be considered "applied" issues. I'll try to address them both.
Is this site about pure economics such as theory?
I think this site should definitely include theory. There is such a thing as an economic theorem (the welfare theorems and Edgeworth's limit theorem come to mind, but there are many others), and an economics.SE site would be woefully incomplete if it didn't allow discussions of such theory. Keep in mind, however, that economic theory is often very quantitative. I asked about this in another question because I feel that quantitative questions should not be excluded.
How about other fields related to economics such as stock, money flow,
investment trend(what kind of investment should we choose in different
time, for example: when the economy is in recession, people tend to
invest in gold, and why people choose to invest in gold)
These are certainly economic issues, but questions about choosing investments and the costs/benefits to choosing them should be asked on the Personal Finance and Money site. The issue with subjective questions like this on a site like economics.SE is that a) every pundit, and therefore every person, "knows the answer" and has subjective interpretations of the data to back up their conclusion.
I think questions about why the economy is in a recession could have several types of answers. The standard explanations could be an option, or references to published papers, studies by the Federal Reserve, etc. could be another option. The latter, however, can get extremely technical and outside of a layman's understanding of economics. I think such questions and both types of answers should be welcome, but I'm worried that people will reject the latter types of answers as too advanced or too technical, even if it's more accurate.
In the second case, what sort of answer would you prefer?