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Was this a recent transplant move? Your plants will need some additional watering the first few months until they become established or during dry spells. Also, make sure the soil is well draining. If the plants are in soggy soil, they could suffer root rot. Your plants could still be suffering some transplant shock or adjustment period to new light conditions too.

In the spring, you can give your plants a slow release fertilizer application to help them.

Hostas should stay green until frost if given water in dry spells. If you have a few tattered leaves, cut those out. If you have a lot of crispy leaves, the plant is getting too much sun or you aren't watering it enough. Every plant expends a lot of energy in making blooms and needs to recharge the batteries, so to speak.

September is a good time to transplant both of these plants. If you have never moved a peony before, take care. The roots break easily. Cut the foliage to the ground. Prepare the new site, mixing in compost. If you are in the upper midwest, set the "eyes" 2 " below ground level and closer to ground level in the warmer parts of the midwest. Planting eyes too deeply may inhibit blooming. Firm the soil as you go and water thoroughly. Mulch for winter and make sure the soil doesn't dry out this fall. Hostas are more forgiving but it makes since to add compost to the site when you prepare it. Plant at the same level it was. It isn't necessary to cut down the leaves prior to transplanting but trim off any burnt, tattered ones.

There are several forms of rot which can affect hosta foliage. Check whether your plant's symptoms match any of those listed in these articles:

https://extension.psu.edu/pests/plant-diseases/all-fact-sheets/hosta-diseases
https://www.gardeningknowhow.com/ornamental/foliage/hosta/hosta-plant-diseases.htm

Rot can also be caused by overwatering, especially with plants in containers.

This sounds like a nitrogen deficiency. You will need an all-purpose fertilizer to apply to the area. Dolomitic lime would be good to add to keep the pH stable, as well as give the plants calcium and magnesium.

Here is a link that will help: https://www.gardeningknowhow.com/ornamental/foliage/hosta/growing-hosta-plants.htm

Generally, you will want to keep all dead growth off of the plant. You can prune those leaves at any time. the flowers can be cut to promote leaf growth, or you can leave them on until they are dead.

At the end of the season in late fall or winter, you may cut back all of the leaves. In fact, this will help the plant out some, too!

Here is an article with more information:https://www.gardeningknowhow.com/ornamental/foliage/hosta/cutting-back-hosta-plants.htm