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When the spathe first forms it is green just like the leaves.
As is prepares to open it begins to change from green to snowy white.
As the spathe matures and starts to fade it once again turns green and eventually will fade to yellow and brown when it completes its cycle.
This color change is due to chlorophyll.
Because the spathe is a leaf it preforms photosynthesis, the process of the plant absorbing sunlight.

https://www.gardeningknowhow.com/houseplants/peace-lily/peace-lily-plants.htm

Peace plants (peace lilies) don't need as much water as many other houseplants. To determine when your peace lily needs to be watered, simply feel the top of the soil and water the plant if the soil surface is dry. Be sure not to water if the soil is still wet, because this can harm the roots. Also make sure the plant is not in a too-large pot for its size, since this will cause the soil to dry out too slowly.

No, you can not root the leaves or flowers. Propagation needs to be from a division of the rhizomes.
The plant can gently be removed from the pot and a rhizome be cut from under the plant.
The rhizomes can be divided into sections, making sure each section has a bud attached. These sections are then potted up individually.
Keep the newly planted rhizomes moist and in a warm location.

https://www.gardeningknowhow.com/houseplants/peace-lily/peace-lily-plants.htm

You may have determined the cause yourself for the yellowing leaves on your Peace Lily.
Peace Lily prefer to be tighter in a pot. To large of a container can lead to root rot.
I would reduce the size of the container on your plant. Trim away the dead plant material and give the plant time to adjust.
Do not over water. Only water when the top inch or so dry out.

Here are some links with more information.
https://www.gardeningknowhow.com/houseplants/peace-lily/repotting-peace-lily-plant.htm
https://www.gardeningknowhow.com/houseplants/peace-lily/peace-lily-plants.htm

Leaf spots can be due to fungus issues.
Make sure the plant is not overwatered, and that excess water is draining from the soil.
Avoid splashing water onto the leaves.
Here are some links with more information.

https://www.gardeningknowhow.com/plant-problems/disease/plant-leaf-spots.htm
https://www.gardeningknowhow.com/houseplants/peace-lily/peace-lily-leaves-yellow-brown.htm

Peace Lily do like to be a bit root bound, though if the roots have taken up all the soil the plant can have trouble taking up water and nutrients.

Make sure you used a new pot size that was 1 size larger then the existing pot.
The soil should be a good quality potting mix and make sure the excess water is draining from the container.

To large of a container can lead to overwatering and root rot. The yellowing leaves generally are indicating a watering issue; too much or too little.

Check the soil, instead of watering on a schedule. Water only when the soil is dry.

You may want to lift the plant and allow the soil to dry. Then it would be good time to determine if the pot is the correct size.

https://www.gardeningknowhow.com/houseplants/peace-lily/repotting-peace-lily-plant.htm
https://www.gardeningknowhow.com/houseplants/peace-lily/peace-lily-plants.htm