It depends the best time to prune is in the fall but if you don't mind a hacked bush through the summer you can prune after blooming.

Depends on the variety--but in general you are waiting too long. Hybrid tea roses (which look like florist roses) should keep 5 or 6 days. Slender buds with few petals may be cut as soon as the sepals start to separate. Fuller buds of HT type may be cut when the outer petals start to separate. Old and old-fashioned roses with many petals (David Austin) open faster and easier than you would think. Generally, these are best cut when the sepals have first dropped and before petals start to separate. Some need to be left on the bush a little longer. If the rose opens wide and shatters or wilts within a day or two, you cut it too late. If it fails to open, you cut it too soon. So observe and adjust--the generalizations above won't always hold. Some rose varieties are long lasting (including all florist varieties) and some are only good for 3-4 days.

If it's going into an attached garage, just throw it out there. You'll find elaborate instructions for getting plants ready to change circumstances, but I've never had anything bothered by moving that isn't a ficus. Plants go in, out, into below freezing temperatures, into hot, dry houses - they don't care. Now the coldest my garage ever gets, is low 20's F. And that's with -20°F and serious wind chill. Below freezing is relatively normal, but it has a hard time getting much colder than that. The roses in the garage have started to leaf out. I need to start watching them, and get them outside fairly soon. My current problem is that there isn't anywhere to put them that isn't covered with snow and isn't in the direct path of cars. I have to at least find the back walk before they can come out. During the spring, they do a fair amount of moving in and out depending on the weather. Our current forecast is for above freezing temperature until Wednesday night, so they could definitely go out for a couple of days. If the forecast low is below around 28°F, or I have reason to believe it is going to get colder than that, they have to get moved back in for the night. If a cold spell comes, and they have to spend a couple of days inside, they just have to. The strange thing, at least IMHO, is that while they start growing so much earlier than the in the ground roses, they don't tend to start blooming that much earlier. Mutabilis has a very hard time beating R. hugonis, and it should be working with a several week head start. There is a definite learning curve with this.

Kali, just in case she does not see your question. It refers to a set of leaves. So you find a set of leaves on the cane that point in the direction that you would like a branch to grow. Right in the nook where the leaf set is connected to the cane on the top side. That is where there are growth nodes that can grow into branches. A rose likes too start new growth from right below where you cut/prune. As that is where the rose will concentrate its growth hormones. Where I live there are an abundance of cane borers. If these are active in your area it is best to place a drop of regular elmers glue on the cut surface. It helps to keep them out of the rose canes.