If anything has dead or dying leaves or flowers always cut them off. That way the plant is not putting energy into that part of the plant. It will also promote new growth. I don't know much about gardening either, but I enjoy my little gardens. I pretty much give everything a prune after it has had a flower. I have not killed off anything yet from doing it. My daisey plants get a full pruning so they just look like stumps and everything else gets a light pruning to were I can see new growth starting. Hope I have helped a tiny bit