How to test the serial correlation of residuals?: Q; Ljung-box test.

How to test GARCH effects?:(1) You can also use the same test statistic but with the squared returns, say. But note that this is a portmateau test, which means that it doesnot have a specific H1(alternative hypothesis). So it may not have ideal power. original form is chi-square, better to use F-form to expect a improved small sample property. (the Lm test of N*R^2 form, or F form)

How to test GARCH effects? (2) Engle's ARCH effect test works for ARCH and GARCH models. Wooldridge (regression-based) has a robust version of this test (robust against to heterscedasticity?). there is also some other technoques (some Austrian guy): robust against the distribution based on probability integral/inverse transform.

test the leverage effects?: Engle and Ng 1993 J of Finance, yes.

I am sorry for that I can not go into the detail since it take me a lot of time and this is BBS where everything is provided for free.

What I also want to say is that BBS is is not a good place to learn econometrics, it is always the textbooks or journal articles.

Furthermore I can not understand "conventional level", significance level? confidence level?

Good luck

You can say "go to ...textbook and .....journal paper to find your answer".

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As a matter of fact, this is correct. My supervisor always tell : you can see ### 1999 paper to have the answer. Nothing wrong with this. When I told him that there is something wrong my GAUSS code, he says: check it again.

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I think it is perfect right to have such answers. The point is he/she tells you which paper which textbook you should read at the first place.