Can I use Pearson correlation for discrete variables? Can I use Pearson correlation for discrete variables, if the level of measurement fits (either ratio or interval).
Thanks!

The correlation coefficient, sure, if you're interested in measuring linear correlation.
If you want to test it, maybe -- you might sometimes need to consider using something else in place of the usual test, though.
The usual test is typically pretty level-robust but for example with count data (and often with other forms of discrete data) you tend to have (a) heteroskedasticity, related to the level of the mean; (b) nonlinear relationships; and (c) changing distribution shape as the mean changes. In particular (a) and (b) might lead to you consider other tests (whether using the same test statistic and a different approach to calculating p-values, or a slightly modified statistic, or even asking somewhat different questions of the data).
