I have several peony rose bushes which have all flowered and now mostly lost their bloom. Is there any way I can dead head them and would this produce more flowers during the rest of the summer?
Not quite sure if I understand - do you have a name for the variety? Are they hybrid tea type or climbers?
Not sure which variety they are, but they're certainly not climbers. After the flowers have fallen they leave behind clumps of 'furry looking' pods! Are these essential to the plant or should I cut them back?
I'd cut them back to the first outward pointing leaf bud below what is left of the flowers. If that means that the rose will be too straggly or too tall next year you can cut to another outward pointing bud lower down.
Do the pods look like these http://farm4.static.flickr.com/3546/3674713163_6fe16c2f08.jpg
Do the leaves look like these http://fc03.deviantart.net/fs18/f/2007/177/d/0/Peony_Leaves_by_nenya.jpg
Do the flowers look like any of these https://www.google.com/search?q=peony+flower&rlz=1C1SVEE_enGB425GB425&tbm=isch&tbo=u&source=univ&sa=X&ei=DoPrUYq1J6iW0AXL2oCIDg&ved=0CFQQsAQ&biw=1241&bih=584
If so these are peonies, not roses. If you don't want to propagate from seed, then cut the seedheads off and leave the plants alone - they hate being messed about with and flower best with benign neglect.
However, peonies only flower once a year, but are glorious when they do