First off, "in their field" has a different meaning from "in their fields".
field (n): a particular branch of study or sphere of activity or interest.
"Use" is a more generic verb that can be used in a wide array of situations, but it's fine in this sentence.
Farmers use chemical fertilizers in their fields.
"Apply" is more specific as it means "to put on the surface of", either literally or metaphorically. Also, the common verb + preposition is "apply to":
Farmers apply chemical fertilizers and insecticides to their fields.
While this is grammatical, it would be more idiomatic to use "spray on", because this is specifically how fertilizers and insecticides are applied.
Farmers spray chemical fertilizers and insecticides on their fields.