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The plants themselves will not winter over, but Cosmos reseeds itself easily.
You can also save the seeds and start new plants in the spring. If the seeds were hybrids they will not likely be the same as the parent plant.

https://www.gardeningknowhow.com/ornamental/flowers/cosmos/growing-cosmos.htm

Many times this is an issue with too much nitrogen, and not enough potassium in the soil. You can offset this by adding fertilizers high in these, with little or no nitrogen. This should correct the issue. This article will help you with the care of these: https://www.gardeningknowhow.com/ornamental/flowers/cosmos/growing-cosmos.htm

Rich garden soil and fertilizer use may delay blooming and encourage excessive leafy growth. There is time left for them to bloom and set seed if first frost isn't before October.

I'm not familiar enough with the climate in your country to be able to tell you whether they will continue or not. I can't seem to find much information on who runs the Agriculture in your area, but I can give you information on growing the plant in question. This article will help: https://www.gardeningknowhow.com/ornamental/flowers/cosmos/growing-cosmos.htm

It can. Usually, it will start to die out, though. This annual will self seed, so it will probably show up again next year. For now, you can enjoy its final stages of life and wait for next year's arrivals.

This article will help you to care for them: https://www.gardeningknowhow.com/ornamental/flowers/cosmos/growing-cosmos.htm

No, it will likely start its die out process, once it expends all of its energy. This is normal. They are annuals and will die, but self seed. You should expect to see more replace it next year.

For now, you can just enjoy its last growth efforts until its death.

This article will give you more information on the plant: https://www.gardeningknowhow.com/ornamental/flowers/cosmos/growing-cosmos.htm