Again, with your data population size and number of variables, you are inevitably going to have a lot of accidental correlations. You'd need an r a lot higher that .16 to start inferring anything more than coincidence
Not really, her p-value is extremely small so randomness is unlikely to be the explanation (unless she tried thousands of relationships and cherry picked this one)
you can easily calculate p value from r and n. After you've looked at enough p-values you can get a sense about what'll be significant just by glancing at the numbers. (input .16 in R, and 13000 in N here: https://socscistatistics.com/pvalues/pearsondistribution.aspx… )