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Although I do not have any pictures to guide you through this, the method is pretty easy. I don't believe you will have any trouble. I will include two articles that will guide you through the process.

This is for wintering elephant ear: https://www.gardeningknowhow.com/ornamental/bulbs/elephant-ear/storing-elephant-ear-bulbs.htm

This is for wintering banana: https://www.gardeningknowhow.com/edible/fruits/banana/banana-plants-in-winter.htm

You will want to plant them both in spring once the soil has warmed up, and there is no chance of frost. Here are two articles on how to store these over winter.

Spider Lily: https://www.gardeningknowhow.com/ornamental/bulbs/lily/overwintering-lily-bulbs.htm
Elephant Ear: https://www.gardeningknowhow.com/ornamental/bulbs/elephant-ear/storing-elephant-ear-bulbs.htm

Although I cannot see the picture very clearly, it appears to look like young scale insects. These are tricky, since they encase themselves in a shell. This prevents many pesticides from working.

The best thing to do from here is to scrape off the patches as often as you see them. There are definitely eggs so you will see them for quite awhile. Once or twice a week, spray with a product called "Force of Nature Miticide" by Foxfarm. (I don't usually recommend products, but in this case, I know that this is one of the few very effective treatments for scale)

After repeating this for a few weeks, there will be no sign of the pest, and the plant will start a very vigorous growth spurt.

This article will give you more information on the care of these plants: https://www.gardeningknowhow.com/ornamental/bulbs/elephant-ear/growing-elephant-ear-plants.htm

Yes, these pods were taken off too early. This appears to be the elephant ear of the genus alocasia, or the mask plant. Although not a true elephant ear, it shares the same name. It is best to take them off after they have dried, fully, on the plant. After that, then you may remove them. and plant them as soon as possible. These seeds will not be viable, and you will have to wait until the next flower pod ripens to do this. Here is an article on how to do this: https://www.gardeningknowhow.com/houseplants/alocasia-plant/elephant-ear-seed-pods.htm

Your plant must be quite a sight. It sounds like it is reproducing and you can start new plants with some of these stolons (look like roots). The other possibility is that your pot is too small. You should go up in size by 2" every year or two. If you don't want the plant to get larger, you should divide it so it won't be pot bound. Remove the entire plant onto a tarp. Wear gloves since the sap may cause skin irritation. Disinfect a sharp knife and divide the clump. Pot them up for friends or compost them. If you don't have a compost pile then add extras to the trash. Don't just throw them out as they are becoming invasive in parts of zones 8-10. I wouldn't simply remove the wandering roots. The plant is telling you that its pot is too small. These articles go into more detail.
https://www.gardeningknowhow.com/ornamental/bulbs/elephant-ear/dividing-elephant-ears.htm
https://homeguides.sfgate.com/elephant-ears-pots-95332.html

Wait until the soil warms up. Putting a tropical plant in cool/cold soil is a recipe for bulb rot. But you can start your plant indoors and move it to the garden after your frost free date. Elephant ear can tolerate full sun if they get lots of moisture when temps go over 85 F. Here is more information: https://www.gardeningknowhow.com/ornamental/bulbs/elephant-ear/growing-elephant-ear-plants.htm