Roses come in several forms, including modern shrub, climbers and ramblers, old garden roses, and modern ever blooming such as hybrid teas, grandifloras, and floribundas. One key about all of them is that they should be pruned in early spring. You can certainly prune off any branches you would like to shape during the summer.
SPRING PRUNING OF ROSES
After the last frost has past is safest to cut into the plant without causing any form of cold damage. You can also base your pruning off of bud growth. When the buds have begun to swell, it is normally a sign to begin pruning. April or May is probably a good time to plan to prune your roses in the Chicago suburbs area where you are located.
FALL PRUNING OF ROSES
You can prune your roses in the fall, so that they are smaller and easier to protect in the winter with a cover. You should cut off just enough to fit them in the cover. Where you make your cut, expect the branch to die back further from winter injury as the branch will be less cold hardy by the pruning cut.
ROSE NOT BLOOMING
Regarding your second rose question, if you thought you removed the rose, it may be that you did remove the entire rose above the graft union of the plant. This is the point where they attach they rose variety you want (with the pretty flowers) onto a rootstock of a rose you don’t want (no pretty flowers but strong grower of roots).
If this is the case, I would recommend you dig out all the roots as the plant will never be what you want. Note though, more roses these days (especially shrub roses) are being grown on their own roots and therefore what is growing back is indeed the plant you want.
SUN OR FERTILIZER
Roses don’t flower for two main reasons, not enough sun or not enough nutrients. If your rose is in the shade, dig it up and move it to a sunnier spot. The second reason is easier to fix. Fertilize your rose with a good quality rose food. Look for a granular or a liquid fertilizer that mentions roses and you should be fine. Don’t use fertilizer spikes (for anything they don’t work well). I would try the fertilizer first and you may be surprised. Roses are heavy feeders and most people don’t fertilize them enough. Often a little rose food is all they need.
For more on rose fertilizer.
Source: Your Garden Sancutary