Take extra care for about a week until you transplanted rose has adjusted to its new home. Mulching always helps to protect the roost and prevents the soil from drying out too quickly. All rose respond better if fertilized frequently. Miniature rose like a feeding of any balanced fertilizer about once every 3 or 4 weeks. A liquid type is usually more useful to the plant immediately, but don't make the solution too strong.
Prevention is the recommended method of control, especially when it comes to diseases.
Again, it is recommended that you check a good rose reference book for you specific problem, and the recommended method of control. Always have your plant well watered before you spray however. Your rose can be pruned at any time of the year. You actually do this whenever you pick a flower. Don't allow long branches to develop on their own, but rather, keep the plant shaped as it grows.