The nutrient cycle is the repetitive passage of a particular nutrient or element from the environment by one or more organisms and back into the environment.
Nutrient recycling involves both biotic and abiotic components like air, water, soil.
Recycling of Carbon, Hydrogen, Nitrogen and Oxygen occurs in water, air and soil, whereas calcium, phosphorus, potassium, etc. are recycled mainly in soil and are available locally.
Ecosystem service is any positive benefit that wildlife or ecosystem people provide.
Yes, nutritious cycling is an ecosystem service. Cycling nutrients is essential for a self-sustaining ecosystem.