Firstly, apart from growth curve and background correction of microarray, what situation else we need to/could do log transformation to handle data? why?

Article Log-transformation and its implications for data analysis

2.1 Using the log transformation to make data conform to normality

2.2 Using the log transformation to reduce variability of data

The log transformation could make the data becoming normal distribution because almost statistics are based on the normal distribution, and log transformation would not change the relative magnitudes of all data

Why/How do I know that my data is based on normal distribution? Or, how do I judge if my data is based on normal distribution?

You could plot the data and to see the distribution