Pests and diseases: Prevention is the best way to avoid pest and disease problems. Start with disease-resistant varieties, keep plants in healthy condition (well fertilized and well watered), maintain good air circulation, keep foliage dry, and remove any diseased foliage or spent flowers. For Japanese beetle grubs, use beneficial nematodes or Milky Spore (Bacillus popilliae). Rose Rx is effective against scale, spidermites and aphids. For more information, see the Pest and Disease Finder.
Black Spot: Rose plant leaves with black spots that eventually turn yellow have black spot. This is often caused by water splashing on leaves, especially in rainy weather. Leaves may require a protective fungicide coating, which would start in the summer before leaf spots started until first frost. Thoroughly clean up debris in the fall, and prune out all diseased canes.
I too, have tried the cut rose flower method, but haven't yet been successful--perhaps because there are chemical additives that the roses have soaked up, or because there are no nodes (which are the points where new shoots grow out), or because the stems have spent much of their energy producing the flowers...BUT, perhaps if the flowers were immediately cut off and some rooting hormones applied to the bottom cut ends, that may work.
Hybrid teas and floribundas usually grow no more than 2 to 3 feet high. Their form is coarse, and hardly very appealing, but they do have the ability to produce an abundance of flowers throughout the growing season. The hybrid tea has large, single blooms on long, stiff stems, whereas the floribunda has slightly smaller clusters of blooms on stems that are not as stiff.
There will be disappointments along the way, when many rose seeds fail to germinate, or perhaps they do germinate, only to die several weeks later from damp-off disease. Sometimes a rose seedling will turn out to be as ugly as sin, or very sickly, and you will reluctantly have to throw it away. Other times they will be just ho-hum, or look too much like its parent, and therefore have no value. But, just when you don't expect it, you might discover that one of your rose seedlings turns out to be very special.