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Gypsophila is considered a sun-lover. Here is an article about them: https://www.gardeningknowhow.com/ornamental/flowers/babys-breath/growing-babys-breath-flowers.htm

Here's an article on growing baby's breath: https://www.gardeningknowhow.com/ornamental/flowers/babys-breath/growing-babys-breath-flowers.htm
You can try bringing them indoors, I have seen a reference to growing them indoors for flowers during the winter, but I think it most likely that they will die back for the winter. But if you gather seeds and replant them in the planters in the spring, you could keep them going in the same containers almost indefinitely.

I am sorry, you would not be able to propagate roses or baby's breath from fresh cut flowers.
Starting a cutting garden can be easily done both with seeds and plants.

Here are a few links to help you get started.

https://www.gardeningknowhow.com/special/spaces/growing-cutting-flower-gardens.htm
https://www.gardeningknowhow.com/ornamental/flowers/roses/starting-a-rose-garden.htm

Annual Baby's Breath will bloom one time, mid summer.
Perennial Baby's Breath will bloom for a longer period--generally also beginning around mid summer.

Depending upon the growing conditions and weather, the bloom time could go into the late summer or early fall.

You could cut and dry the Baby's Breath for your Oct 1st event.

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

Look for annual Baby's Breath seeds, you can start indoors or direct sow outdoors after last frost.
It is very difficult to time blooms as it depends greatly on growing conditions.

Read the seed packets; they will have a range of time from germination to maturity.

Avoid a perennial seed, as they can take up to 3 to 5 years to bloom.

You may also be able to find plants at the garden center that would give you a head start on growing.

I would also encourage you to not stress to terribly much; Baby's Breath is readily available at floral shops and is relatively inexpensive.
If your garden plants don't quite preform you can still have the beauty of Baby's Breath.

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

Wait till the weather warms up and the seedlings are actively growing to fertilize.

The yellow leaves may be due to the cooler temps. Here is more:
https://www.gardeningknowhow.com/garden-how-to/propagation/seeds/seedlings-turning-yellow.htm