I'm not sure what you mean when you're talking about stems.
Dendrobiums have canes, which is the stalk that leaves grow from. They can also have spikes, the stems flowers grow on, which grow out of the canes, usually near the leaves. I would not cut down the canes, ever, unless they look diseased or rotted. Spikes, you can trim once the flowers die back, or allow them to die back on their own, which is what I do. I don't think dendrobiums rebloom from old spikes, like phals do, but I'm not sure. Hopefully someone else will come along that can answer that question for both of us.
As far as the care, it really depends. I have one NOID Dendrobium that turned out to have care pretty similar to phals. I have another one that likes to be watered on the same schedule as my paphs and oncidiums and likes slightly brighter light than phals. There are some that are TOTALLY different from that. There's a lot of diversity in dendrobiums.
Some dendrobiums, I think they are referred to as nobiles, require a winter rest. I avoid these, because I'm just not sure I would do the winter rest properly. I don't THINK yours is one of these, but you should probably do some research on your particular hybrid and find out.
I did look up some pics of your plant in bloom and it's beautiful. I think that it's probably going to have similar care to mine, which is phal light and watering requirements.