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Dig the bulbs when the foliage is dying back. This may be after your first frost.

The soil may be staying too moist. Although elephant ear does like its soil to be kept evenly moist, excessively moist soil can promote fungal growth. It will need less water now that it has been brought indoors. Experiment with watering schedules until you find a balance. Also avoid getting the water on the leaves when you water.

I would recommend Neem oil to keep bugs away from your plants. Just don't spray them in full sun. Wait until a cloudy day, or afternoon. This article will give you more information to their care, in the meantime: https://www.gardeningknowhow.com/ornamental/bulbs/elephant-ear/growing-elephant-ear-plants.htm

I think your best bet here would be to store them in the warmer location until the temperatures get back up in the original spot. This will keep them alive until planting time.

Here is an article that will help: https://www.gardeningknowhow.com/ornamental/bulbs/elephant-ear/storing-elephant-ear-bulbs.htm

As long as the leaves are green, let it be. You didn't say what climate zone you live in, but most types of elephant ear (Colocasias, Alocasias, and Caladiums) prefer more tropical conditions. Some species tolerate brief or moderate periods of cold, but most do not. Also, may species go into dormancy for a few weeks or months.

Colocasia "Pink China" appears to be the most cold-hardy elephant ear. It can survive the winter in zone 6 if you cover the ground with mulch to give it some protection. All the other elephat ears should be able to grow in zone 6 as well, but you'll have to dig up the tuber in the fall and store it indoors, since otherwise it will freeze during the winter. Here's how to overwinter them:

https://www.gardeningknowhow.com/ornamental/bulbs/elephant-ear/storing-elephant-ear-bulbs.htm