For the most part, miniature roses are scaled-down versions of full-sized roses, and while they vary in many ways, all mini roses have small, rarely fragrant flowers. All can be traced back to a common ancestor, the China rose (Rosa chinensis minima). Did you know? The Guinness Book of World Records reports that the Tombstone Rose, America's largest rose bush, was first planted in 1885 in Tombstone, Arizona. Not a miniature rose per se (actually a “White Lady Banks" rose), its flowers are tiny. With a trunk six feet wide, its white blooms cover 9,000 square feet of trellis!
Just like your regular roses, yes, these minis would love to be pruned. Go ahead and shape them how you please.
Damp conditions can cause blackspot to develop on the leaves. It's a fungus that needs to be treated right away. Cut off affected leaves and treat the leaves with a fungicide especially made for blackspot. Good air ventilation will also help to prevent fungus,
Yellow leaves that drop off can be a symptom of a few things. Lack of sunlight, dry soil, and dry air will cause roses to shed their leaves. Continue to take good care of your miniature roses and follow their requirements on water, light and fertilizer, and this will help them recover.