Regarding the following sentences that you presented:
“The company conducts a research on/about fecund mango production.”
“The company conducts research on/about fecund mango production.”
The idiomatic usage is the second sentence without the article “a” before “research.” The first sentence with the article “a,” although grammatically unassailable, sounds stilted. In such situations, it’s advisable to go for the better-sounding sentence.
There’s also a difference in the intended meaning of the two sentences. The first sentence (with the article “a”) denotes a particular and specific research study on fecund mango production; as such, it can be better stated with the word “study” after “research,” as follows: “The company conducts a research study on/about fecund mango production.”
In contrast, the second sentence (without the article “a”) means to say that the company does research on fecund mango production as one of or among its operating activities. The word “research” is used in a generic sense and doesn't refer to a particular research study, unlike in the first sentence.