Never fertilize a newly planted rose. Did you lose a lot of soil from the root ball when you planted it. If so, many of the feeder roots fell off with the soil. Your rose will take a while to grow new feeder roots. Until that happens, it can't take up sufficient moisture. Peat, unless it's saturated prior to mixing with the soil can pull moisture from the roots also. There are other organics that work better. Like Hoove said, it'll take awhile for your bush to adjust to it's new home. Keep it watered and don't try to fertilize it until it recovers and begins growing again. Meanwhile cut off the old flower buds so it can concentrate on making roots, not flowers. It needs a good root system to support good growth and blooms.

I haven't done this but suggest you take your hose and wash it off. If you happened to do it on a hot day you may have burned some leaves. It may shed a few leaves and pout but I doubt it'll die. Water as usual but don't fertilize until you see some new growth.

You can just snap the spent flower off. I try not to remove leaves from young plants-- they are needed for growth.

Our heat has been pretty high the last couple of weeks. I have many new bushes from one and two gallon pots that I planted this spring. All are own root. I check the ground an inch down before I water. If we get less that a quarter inch of rain I usually have to hand water using a wand every two days. If we get more than one quarter inch rain I wait until three to four days after the rain to water. I do have mine in beds with no grass or weeds and it is mulched so the water doesn't evaporate as fast. The key is how quickly is your ground drying out then set up a water schedule based on that. My schedule works great for me.