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Drooping stems could indicate the plant is becoming weak from excessive moisture or root problems. Make sure the soil is well-draining in the planting location. Otherwise, the plant could be drooping if it's grown too "leggy" because of over-fertilization or low light.

This article will help you with care of your plants.

https://www.gardeningknowhow.com/ornamental/bulbs/rain-lily/growing-rain-lilies.htm

Yes, but this is very difficult. It is recommended that you grow them from splitting up the bulbs.

Here is an article with a little more information: https://www.gardeningknowhow.com/ornamental/bulbs/rain-lily/growing-rain-lilies.htm

Really, you want to plant these in the fall, but this all depends on where you are located. They need a cold period to break dormancy, so if your area will still remain cold then you should be able to plant now.

Here is an article for more information on these plants: https://www.gardeningknowhow.com/ornamental/bulbs/rain-lily/growing-rain-lilies.htm