Answer: Based on your description I am not certain what is happening. The hydrangeas bloom on old wood, so avoid pruning them in the fall or spring. It is possible they have been losing buds or branches due to winter cold, or they may need more sunlight. These plants need morning sun or bright dappled light all day in order to set buds. In too shady a spot they will not bloom. Hydrangeas can also benefit from annual top dressings of compost and a spring application of a general purpose slow release granular fertilizer. If they never bloomed, they may be a variety that is root hardy in your area but not bud hardy -- some are simply better suited to your climate than others.
Azaleas need an evenly moist yet well drained soil, meaning damp like a wrung out sponge. The soil should be organic and humusy. Like the hydrangeas, they will benefit from a year round organic mulch to help keep the soil evenly moist. Azaleas do best in all morning sun or bright dappled light all day. In too much shade they will grow thin and leggy. Azaleas are not heavy feeders but can benefit from annual topdressing of compost along with a spring application of fertilizer formulated for acid loving plants. Look for a slow release granular fertilizer such as Hollytone and follow the label directions.
The peony would do best in a location with full direct sun all day long. Sometimes over the years nearby trees grow and shade what used to be a sunny spot, so perhaps this has happened to yours over time. If this is the case you could transplant it in the early fall. In the meantime, topdress with compost and apply a general purpose granular fertilizer such as 10-10-10 per the label directions. Mulch around the plant and water deeply if there is a long dry spell of several weeks.
The gray would probably be mildew. Some years are worse than others as far as disease problems such as this, it is somewhat weather related. Make sure the plant is not crowded because air circulation can help prevent this type of problem. Also avoid watering in the evening, and avoid wetting the foliage. If you have to water do so in the morning and apply it directly to the soil. Every fall, after frost, clean up all the old peony stems and leaves and put them in the trash. This can help reduce reinfection from year to year. Do not cut it back until frost has killed the stems and foliage, this plant needs its foliage through the summer.
I hope this helps.
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