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Your Peace-lily (Spathiphyllum cv.) wants indirect light, mild temperatures, regular water with reasonably good drainage, and light fertilization. Some humidity in the air would also be beneficial. First unpot the plant and examine the conditions of roots, soil, and pot drainage. Roots should be white and firm. The soil should be moist but not saturated. Drainage hole should not be blocked or submerged. When planning to irrigate the plant, first check the soil moisture, Let it become partly dry before watering. Spathiphyllum can take low light conditions, but there are limits, if the plant is ailing, place it in somewhat brighter light, near a window.
Spider Plants (Chlorophytum comosum) can keep a large number of attached plantets ('babies') on indefinitively without any harm.
As long as the plant is healthy, the plantlets will just behave the same as any other leaf or stem.