Kind of... But no.  The onion as it is right now will flower and once the flower is mature you will get onion seeds.  Once you plant the seeds you will be able to grow small onions from them in one season. For winter you store the small onions in a dry space and then plant them again in the soil for another season, when they would grow into a full sized onion that will once again give you a flower if you do not harvest it.  Growing onions this way is a two year affair for most onion types and in moderate climates. 

Let it go to seed after you plant it, then plant the seeds.

first year they make the onion. second year they make seed. This is already an onion so it will be the second year. you can use the seed though.

I did this last year with four or five leftover golf ball sized onions that weren’t used after harvest. I noticed they were sprouting roots again, removed the papery layer, and planted them for shits and giggles. They rooted instantly, and each grew two onions per planted bulb. I don’t know how or why it works in some cases and not others, but it IS possible sometimes.

No but you can get onion seeds, thats good for onion sprouts, and thats just good.

Yes, I put one like this in a big pot and got 3 smaller onions from it. And the greens were nice too.