1. One of them is: whether a chi-square depends on the sample size or not, and why?

Well, I understood that chi-square uses counts and frequencies as data rather than standard deviations and means, and with it data is analyzed in categories, but I still cannot reach to a clear conclusion whether it depends on the sample size or not.

2. Another problematic question I have is: which null hypothesis does the regression analysis usually use?

As far as I know, there are two null hypothesis: a directional and a non-directional one. And I think that it is the non-directional null hupothesis, because it tests differences or relationships, and it is relationships between variables that a regression analysis tries to explore. But this is just my opinion and am not sure if it is really the case – If somebody is sure about the correct answer, please let me know

Thanks in advance!