Is this rose canker? If not what is it? How to identify canker? My plant's stem has gone blackish at some places and woody in others. I tried looking into the available images on the net for canker, and I am confused if this is simply a woody stem or a canker. Also, how should a healthy 5.5 feet tall rose plant's stem look like? Green? Woody? Blackish?
Not canker - older rose stems often look like this, and the short piece of dead stem showing in the top picture is just a bit of die back, normal when a shoot has been removed improperly (meaning you didn't cut back to an outward facing bud on the stem, probably). And it happens anyway sometimes, nothing to worry about, though in this case, I would probably remove the top of that stem, below where it forks into two directions, to an outward facing bud or growth point.
When planted in open ground, roses with stems that look like this often throw up new shoots from the base, and as they grow on, the older, less productive stems can be removed. However, I note all the other plants in your picture are in pots, so if your rose is also potted, its unlikely to put out new, lively stems from the base.
Sometimes die back can progress to canker - usual treatment is to remove affected stems as soon as you notice them. Prevention is better than cure, so good pruning techniques are important, as is using tools with cleaned and sharp blades (loppers and secateurs). More info in the link below