They are definitely
old enough enough to be neutered and spayed. That's the only way to prevent unwanted litters of kittens. Kittens can and do
reach sexual maturity as early as 4 months. I myself had one kitten that did that.
Unfortunately at the time the vet refused to spay until she underwent her first heat cycle. I was nevertheless furious as a heat cycle places a large amount of stress on a female cat, and in this case completely unnecessary.
Also during a heat cycle, the personality of your cat may change. Rather than choosing to stay indoors, she may want to bolt out of the door in an effort to get mated, however in your case, she may not need to.
I cannot stress the importance enough of neutering and spaying kittens and cats when one is not a registered breeder.
Your three kittens will need something of their own to climb on such as a cat tree or cat condo. Not to mention something to scratch as well. Scratching is a natural instinct for kittens and cats. And be prepared to experiment, some cats prefer particular materials to scratch on. The most common materials out there include, sisal rope, carpet, and wood.
As for climbing up the curtains, you could try washing the curtains in a citrus scented laundry powder/detergent. What a friend of mine actually did was wash her curtains and lounge fabric in dishwashing detergent that was citrus based or scented. Cats generally do not like citrus scents and will stay away.
Discourage the kittens from playing there in the first place by providing toys, (again be prepared to experiment as well), whether they be toy mice, feathers, various other stuffed toys, balls, etc or even the cardboard box that everything came from in another area of the house/room.
Also have a few toys on hand. When they do approach the curtains to play, throw a toy past them or just out of their reach to distract them from the curtains and encourage them to play with the toy. Kittens are easy to distract.
You could also place helium balloons tied to a weight like a can of beans or a book under/near the curtains where the kittens play. A sudden movement of the helium balloons towards them while they play may frighten them away. However this isn't such a good idea if this window is where they watch the world go by from the inside.
In this case, revert back to the toys.
If you do use a spray bottle. Use only water. And only spray somewhere near the kitten, not
at the kitten. Use it as a distraction device, not a punishment device. Kittens and cats do not respond well to punishment. Rather, they need to be shown a better alternative.
Good luck and welcome to TheCatSite, (TCS).