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The ideal time to prune roses is just as they are leafing out in spring. When you see buds swelling, it is time. An old saying is to prune roses when the forsythia blooms. I find this a week or two too late where I live. It takes lots of plant energy to leaf out. Allowing the rose to leaf out and then cutting off those new leaves is stressful to the plant. Any time you notice dead, diseased, dying or damaged canes, they should be removed promptly. https://www.gardeningknowhow.com/ornamental/flowers/roses/pruning-roses.htm

Northern gardeners also enjoy hybrid teas! You may have what we call "winter die-back" of the cane tips but typical spring pruning will remove these. If you have already done spring pruning then clip any tips that have died. Unless you have a particularly sensitive variety, frost won't set your roses back much.

The crossbreeding of roses is quite a process. Probably best to contact a commercial rose grower like Weeks Roses to get the best information. Here is a link to their Contact Us page where you can submit your question: http://www.weeksroses.com/contactForm.php If you have trouble and do not hear from them let me know and I will do my best to get you connected with them.

If your plant has leaves, wait to put it out until forsythia is blooming. Get it used to the outside and to full sun gradually over a week. Despite the best care, expect transplant shock - some leaf loss and a droopy appearance for a few days.

It looks like your rose is in regular soil while in a container. This is a mistake since regular soil compacts in containers, inhibits root growth, and prevents adequate air and moisture movement in the soil. Except for miniature roses, all roses perform better is planted and not potted. Roses also need bright direct sunlight; 6 hours is the minimum. There are also heavy feeders. How much and when to apply fertilizer depends on what you use -follow the instructions - but starts in spring with leaf break and is repeated several times during the growing season. The last fertilization is 30-45 days before the first frost date. Proper pruning is also necessary for a healthy plant. In your case, I would replant into a larger container using potting soil mix (no actual soil - mostly peat or coir and perlite) and compost. Mix them half and half. Use a hose to gently remove the garden soil. Here is a humorous look at fertilizing: http://www.rose.org/rose-care-articles/fertilizers-when-and-how/

This article will give you some ideas: https://www.gardeningknowhow.com/plant-problems/pests/deer/deer-repellents.htm