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The flowers will eventually start turning color with age.

This link will help you.
https://www.gardeningknowhow.com/houseplants/peace-lily/peace-lilies-getting-brown-tips.htm

Although they can tolerate being slightly dry, it is best to keep them moist. Not wet, or dry but in between. they need to be in a bright window for at least 4 hours a day, But they can't stand full sun, or be too bright for too long. Here is a link on their care:

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

This happens because the white structure that appears to be a flower petal is actually a type of leaf called a spathe. The actual flowers are tiny and found on the spike-shaped structure. Each spathe will go from white to green as it ages and reverts back to being a photosythetic leaf.

To prevent your plant from being full of green "flowers," you can cut off (deadhead) the flower spikes that have green spathes. This will encourage the plant to produce more flowers.

More than likely, yes. More specifically the soil is either too nutrient rich, or has a fungal/bacterial infection. I would add a little wettable sulfur to the soil to kill any infection, or prevent it if the soil isn't infected.

These don't need feeding often. Especially if there is already slow release fertilizer in the soil. Also, make sure not to over water the plant. This could cause fungal infection. Water when the first two inches of top soil is dry.

Here is an article for more information: https://www.gardeningknowhow.com/houseplants/peace-lily/diseases-spathiphyllum-tips-treating-peace-lily-diseases.htm

I believe you can save this plant. Remove all the dead and dying material. Remove the plant from the container to figure out if something is wrong there. Is the plant root-bound leaving little soil in the pot? Are any insects evident? You might briefly soak the rootball - just a few minutes - to flush the fertilizer and any insects and then repot in a regular potting mix. If you are in the northern hemisphere and heading into winter, only fertilize every 6 weeks until next March or whenever you see it perking up with higher sun/light levels. Peace lily likes a bright spot but not direct sunlight; it likes moist but not soggy soil so don't water if the top inch is still damp; and if your home has dry air, mist the plant between waterings. WikiHow has a nice article with pictures and this website discusses care and repotting: https://www.gardeningknowhow.com/houseplants/peace-lily/peace-lily-plants.htm