The * parts of the litanies, are these words repeated throughout the entire section? Or just for the lines with the *?

Yes, you are to repeat the invocation until it changes. The asterisk is to indicate this. It's just a way for the printer to save on ink and space. So: Morning star, pray for us. Health of the sick, pray for us. Refuge of sinners, pray for us. And so on until another set of text, at least in the image attached, is written in italics.