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This article should help: https://www.gardeningknowhow.com/ornamental/flowers/peony/powdery-mildew-peonies.htm

The fungi can actually overwinter on plant debris, so it is best to go ahead and get rid of the fungal disease now to prevent future outbreaks.

Peonies are finicky in their blooming. Any disturbance can make them skip a year. What I think likely happened is that one year the pink bloomed and the white failed to and the next the white bloomed while the pink failed to bloom. I also have a multi-color peony bed, and never know which plants will bloom in any year. Some years they all will go and others only one will open. A million different stressors can cause this.

It may seem like they are sectioned off in particular places, but if they are a well established peony bed, then the tubers have grown into their neighbor's beds. So, where you may have planted white a few years ago, if the pinks are nearby, they have spread into the white and vice versa.

Try to reduce stress to the plants as much as possible. Make sure they are getting enough water and light, that the turbers are not being buried too deeply by mulch, that they have enough nutrients and, importantly, their roots are not being disturbed in any way. this should encourage all colors to bloom at once.

Peonies are very finicky when replanted. It may take them a year or two before they recover from transplant shock. They may have a fungus too. Treat the plants with a fungicide to help this.

This article will help you with propagating peonies: https://www.gardeningknowhow.com/ornamental/flowers/peony/dividing-peony-plants.htm

Peonies hate to be transplanted and can take years to bloom after transplanting. In fact, it may take them a year or two before they recover from transplant shock. However, if you really want to move them, early fall is a good time to dig up or transplant peonies. Make sure you get as much of the root system as possible and replant in a sunny location in well-draining soil. Keep them watered as the roots establish. This article will help with peony care: https://www.gardeningknowhow.com/ornamental/flowers/peony/peony-care.htm

If you already have them in a suitable location but are simply having blooming issues, your soil could be lacking phosphorus, which is responsible for flowering. Try adding a phosphorus rich fertilizer or bone meal to the soil around your plants and see if this helps.