Prune out the dead wood but otherwise leave her alone. Only hybrid teas need the kind of pruning you are talking about. You can prune to shape her a bit, but it won't do a lot to keep her blooming. Zeffy is not a good repeater and feeding her won't help her repeat much, tho it will keep her healthy. If she is in good soil, you don't even need to feed her. Fertilizing is like vitamins: if the diet is healthy, you don't need supplements. I feed mine once or twice I year if I get around to it.

Catsrose is correct. Only prune lightly and clean her up by removing spent flowers. In my soil I have to fertilize two-three times a year, and I only use organic fertilizer.

Some years my Zephirine flowers continuously and with very good repeat, even outperforms my modern roses. For some reason she doesn't perform the same every year, and it might have something to do with fertilizing or weather, I'm not shore. I always give a second round of fertilizing when first flush is about to unfold. I also like the liquid fertilizers with seaweed.

It depends on how you want her to grow. My ZD was left alone and became over grown. Now I do cut back the laterals (the little shoots that come off the main canes that produce the flowers) to the first or second leaflet. Since ZD doesn't really have a good repeat (for me anyway) I usually only have to do this once. I found that if I left it, the laterals got as big as the main canes and the rose was too big. I usually get some die back in the winter and I remove some dead wood in the spring.

I'm not really interested in rebloom with mine at the moment, more than I am interested in it filling my arbor, so I am just cutting out all the weak basal canes, laterals, and then hoping for some new, thicker basals. Based on the reports I've heard about Zephirine.....like most antique roses....the rebloom becomes better as the root network develops which really is a just a matter of time. Mine had very weak rebloom in it's 1st year in the ground last year. It will most likely be better this year, then better the next, and the next, and so on.