Right, don't fertilize until they have recovered and have put out plenty of leaves. Bloom Buster is the wrong kind of fertilizer--regular Miracle Gro or Miracle Gro for Roses is fine, or any reasonably balanced fertilizer such as 10-10-10 or 18-6-12. Watering correctly is the most important thing. Keep a 2" mulch of leaves or bark around the roses. When the soil under the mulch feels dry-ish, water thoroughly with 2-3 gallons for small plants or 5 gallons for larger, plus or minus for extremely hot or very mild, cloudy weather. Usually once a week is fine. For new plants, I divide the ration in half and water twice a week.

Marion, I do the following to root my roses: I like to take the cutting from a branch that has had a bloom that has just finished blooming. I cut it so that I will have 2 sections of leaves, then I cut the spent bloom off the top. I put the cutting immediately into water while I get more cuttings, prepare the soil, etc. I like to use few drops of a product called "Super Thrive" in the water I soak it in, and in the water for the dirt. I use miracle grow potting soil in a small container. I get it wet, but not so much that it will be sitting in a puddle. I make a hole in the dirt with a pencil. I take the rose out of the water, and make a few shallow cuts at the base, then I dip it in Schultz TakeRoot powdered rooting hormone, and stick it in the hole in the dirt. I put the little pot of dirt and rose into a zip lock bag (I like the 2 gallon ones) then I zip it most of the way up, and blow air into it to create a mini greenhouse. I put it in a window that does not get direct sun. In my case, a north facing window. I don't touch it for at least 2 weeks, then I lightly pull on the stem to see if it has rooted. If the stem turns black, it is dead. If it grows mold, it needs to be cleaned off immediately or thrown away so that it doesn't effect the other cuttings. If you are successful, in 2-4 weeks new leafs will start to grow. If you used clear cups for the dirt, you will start to see white roots in the soil. I adapted my method from this video I watched when I first started: https://www.youtube.com/watch?v=LiL83eUKWY8

I think some companies say in fine print that they can substitute roses. I was surprised to read that on some online websites. It is a very unique beautiful looking rose, and rather a nice surprise but disappointing to have no scent, I'm sure. I found this link that looks just like yours and says it is an Alnwick https://davesgarden.com/guides/pf/showimage/296558/#b but I saw a lot of other photos of Alnwick that look nothing like this. Hope this helps.

I have never heard of cutting back a bare root rose at planting unless there is some dead cane to be removed. Pruning of any kind always stimulates TOP growth, not the roots. You can leave all the hips on you want. The rose will not go dormant. It will continue to put out growth until the weather stops it. I've left hips on from the spring flush in June and the rose continued to grow and bloom right through until October. New Dawn is such a growth monster that I can't see any purpose in disbudding it. The roots are growing, count on it! Roses, climbers in particular, will not send up more cane than their root system can sustain. Hence the saying for climbers, first year sleep, second year creep, third year leap. Those first few years that it seems to not be doing anything it is in fact building a big enough root ball to be able to push nutrients up those long canes you're waiting for. Once it feels it has sufficient roots to do that it will begin to climb.