Popular wisdom holds both that "birds of a feather flock together" and that "opposites attract." Which of these pieces of conventional wisdom is supported by social psychological research?

The idea that "birds of a feather flock together" is generally more supported by social psychological research than the idea that "opposites attract." People appear to select friends and romantic partners who are similar to them, particularly with regard to deeply held values, political beliefs, and so forth (though they may not always select people who exactly match them in personality).

What are the factors that influence the power of a statistical test?

The alpha level, the effect size, and the sample size. Some experts argue that all statistical significance really tells you is how big your sample was, as statistical power (or the likelihood of finding statistical significance) is so heavily influence by sample size that with a sufficiently large sample, you are almost guaranteed to get statistical significance even for very small effects, and with a very small sample size, it may be almost impossible to get statistical significance even for a relatively large effect.

When should managers provide feedback to their employees?

As often as possible or whenever there is a behavior they have observed about which they can provide feedback. Feedback should never be a surprise that an employee first learns about when it is time for a formal (quarterly / annual) performance evaluation.