your transplanted rose looks sad becuause you transplanted it during the vegetative season, and maybe you even touched its roots. It is a very common reaction and watering a bit more (without drowning) is good. Although it needs sun usually, after a transplant it is much much better to leave the rose in shadow or half-shadow for a few days. I usually simply take an old umbrella and put it there until the rose looks fine again.
For the future, if possibile, avoid transplanting during this season.

With regards to wintering floribunda roses, I have been told that the best way is to prune them and then cover them nearly completely. As I have 1-2 floribundas only (the rest are mainly rugosas), and as I am in zone 8, I can't tell you any personal experience about wintering floribundas in Z5.

For the future, if possibile, avoid transplanting during this season.

Perhaps that's true in Italy, but now is a perfect time in your area to transplant a rose. I'm fairly certain the Knockout is going through some transplant shock but with careful watering and some protection from the sun it should come back within a few days.

As for the mulch, here it's just at the base of the plant. However, in your zone you may want to go higher, unless the bud union was placed 4-6" below ground when planted, something that also helps protect from cold winters.

One is not supposed to touch roots while planting?

It's better to leave the roots alone as much as possible to protect the feeder roots. If you get a nice, intact rootball and move it gently the rose won't even know that it has been moved. Now it a good time to do it especially if it is still cool out and your area has a rainy spring.

The best way to winter protect a rose in zone 5 is to plant it 4-6 inches deeper than it was in the pot. That way you can protect the graft without doing any extra winter protection. Don't do any pruning in the fall as the cuts from pruning can make the rose more vulnerable to the cold. The chicken wire cage goes around the rose to hold in the mulch and stop rodents from eating the rose during the winter. The mulch then goes around the rose to as high as you want it. The more mulch you put in around the rose, the more green cane you will have in the spring. But you need to also consider how wet your winters and springs are. If the mulch is too wet then it can provide the right conditions for the rose to get canker. Canker is an infection of the rose that occurs mostly in damp spring conditions. I no longer do any winter protection on my roses because I lost more cane to canker than to the winter cold.

As for your transplanted rose, it will be fine. Keep watering it every day or every other day for the first week and every few days after that and it should recover.

As well on the transplanted rose did you cut it back? Before or after transplanting? If not you might do so now. I moved four of mine two weekends ago and cut them down by half. They still looked awful until about four days ago but giving them a haircut will aid in roses recovering.

Hope this helps.

Kate

My George Burns was an own root plant. I let nature blow oak leaves at it base. It requires severe pruning each spring but is 10 inches tall right now and setting buds.
If yours is a grafted plant and you didn't bury the graft when you planted it, you'll have to cover the base and lower portion of the canes with soil or mulch to protect them this winter.
When moving a bush, if the soil falls away from the roots, the tiny feeder roots fall away with it. The bush then loses its ability to take up moisture. Keeping a large ball of soil around the roots prevents this. Cuttin the top growth back to more the size of the root system lessens the moisture needs. New feeder roots grow back quickly but in the meantime the foliage will wilt and you may lose some.