Will Standardizing Variables Make the Correlation 0?

The statement is false. Standardizing the variables will switch the sign of the correlation coefficient. This will only result in a correlation of O if the correlation was 0 before the variables were standardized.

Does standardizing variables change correlation?

Because by definition the correlation coefficient is independent of change of origin and scale. As such standardization will not alter the value of correlation.

Does a correlation of 0.02 indicates a strong positive association?

A correlation of 0.02 indicates a strong positive association. ... Correlation measures the strength of only the linear relationship between two variables. It always lies between and 1.