Isn't your second paragraph just a definition of a false positive?
And, it looks like power is the error rate for false negatives:
https://en.m.wikipedia.org/wiki/Statistical_power
Too late to edit my original to fix this.
And, it looks like power is the error rate for false negatives:
https://en.m.wikipedia.org/wiki/Statistical_power
Too late to edit my original to fix this.
A p-value of 5% means that, IF the null hypothesis is true (IF!), then there's a 5% chance of getting results as extreme as measured.
A p-value of 5% does not mean than you should expect a rate of 5% false positives & negatives.