I don't believe I can fully answer your questions. I have yet to install electricity to our Pergola but have recognized the moisture problems in doing such. From my research, wet-area outdoor fans are not suited to having direct rainfall contact. My thought is to install a large sheet of plate glass on the "roof" of the Pergola to shield the fan and electrical connections. As mentioned, have yet to do this so cannot attest to success.

I'm not thinking pendant lights would be suited - either for outdoors, or for use within a pergola. Too great of a probability that someone will hit them in addition to them not being suited for moisture. And, the taller a Pergola stands, the less shade value you will receive. Here is a photo of my plan to embed rope lighting into the underside of the top rails. I just took this photo this morning so winters dirt and todays rainfall are apparent but hopefully you'll get the idea. Again, haven't done it yet but this is my solution. (The PVC holds a valance for additional late afternoon sun blocking)

{{!gwi}}

Below is a link showing the assembly of and some schematics of our Pergola construction. Good luck with yours.

Here is a link that might be useful: Pergola Assembly