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Not enough light or water can make leaves on calla plants droop or wilt. As for the flowers, what you are seeing is the seed pod of the plant, which can be cut off or, if wanting to propagate the seeds, left to ripen on the plant before collecting the seeds. If it's already yellow and feels soft, then it should be ripe enough to use. Take out the seeds and allow them to dry out some (Note: they may require rinsing with water to remove pulp). They can then be stored after drying or planted right away. Keep in mind that they take longer to mature when planted this way verses offsets.

Yes, callas make good indoor plants, especially if they spend summers outside. Here is some info on growing and caring for calla lily plants that should help: https://www.gardeningknowhow.com/ornamental/bulbs/calla-lily/growing-calla-lilies-and-care-of-calla-lilies.htm

As long as you can keep them well watered as they adjust to their new location, that should be fine.

Root rot is caused by too much water. These plants should be kept somewhat moist, but not overly wet. You can check for moisture by inserting your finger into the soil. If it feels quite wet, then this is likely your problem. You can also check the roots by removing the plants from the pot (this will also let you see how wet it is). Should root rot be the issue, then this article will help: https://www.gardeningknowhow.com/plant-problems/disease/treating-root-rot-gardening-tips-for-housplants.htm

You can transplant them outdoors if you would like. Just prepare the planting hole around the same depth as the pot it is currently in and water it well. Here is an article that you may find helpful: https://www.gardeningknowhow.com/ornamental/bulbs/calla-lily/growing-calla-lilies-and-care-of-calla-lilies.htm

This is typically an indication that the plants are not getting enough sun. I would see if it is possible to get them just a bit more light, perhaps by thinning any plants that may be shading the area.