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If you are using them fresh, then no. If you intend to have them stored for any amount of time, then you will need to cure them. This article will help: https://www.gardeningknowhow.com/edible/vegetables/onion/storing-onions.htm

Onions are biennials, which means they bloom in their second season of growth. As with a lot of plants, they get woody and not very appetizing once they've flowered. It sounds like they just didn't have enough time to grow in their first season. Onions take a while, and should be started indoors before the last frost. Especially if you're growing them from seed, they should be planted 2 to 3 months before the last frost, then transplanted out when the weather warms up.

This article will tell you more about that:

https://www.gardeningknowhow.com/edible/vegetables/onion/find-how-to-grow-onions-in-your-garden.htm

Your onions do not need heavy fertilization. It is best to do half strength all-purpose fertilizer. Onions grow bigger by having more leaves. The more leaves they produced, the bigger the onions will be. If you feel you need a little boost, then go with a higher nitrogen fertilizer.

There is no problem with planting them in containers and keeping them indoors for the winter. This is the best method, and will ensure better production. Here is an article for more information: https://www.gardeningknowhow.com/edible/vegetables/onion/growing-onions-in-container-gardens.htm

No, once you harvest an onion, unless you physically saw replacement bulbs near it, they will not grow back. You will have to reseed, or you can use the bottom root portion of the onion once you use the onion to replant. That root section will turn into a cluster of onions if planted correctly.

This website will help: https://www.instructables.com/id/Grow-Onions-from-Discarded-Onion-Bottoms/

You can, but these are pretty hardy, and will continue to grow just fine if you leave them. With a layer of straw mulch, you can extend the harvest. Depending on your variety... (the spicier the onion, the more sulfuric acid is present.) The sulphuric acid content of the onion can act as an "antifreeze", and even though they may sustain some damage, they will certainly not die from this.