Yes, ideally the fan should be centered in geometric center of room, but when push comes to shove it absolutely needs not be of couse, but i think a ceiling fan that is not centered and a chandelier that is centered will not look good

I am looking for pendant lighting for over my vanity and a flushmount light to match for the ceiling

Hope is patience with lamp lit !

pendant lights looks nice only if place above a table like a breakfast nook or island. hanging them freely does not complement their look. since there is no island under the ceiling try to embed recessed lights in the ceiling. alternatively track lights will also look great if you need brightness.