When, why and at what instance Narada Muni was cursed by Prajapati Daksa?
The story is told in this chapter of the Srimad Bhagavatam. Daksha had 10,000 sons called the Haryaśvas, and he instructed them to populate creation with more beings. But then Narada convinced them to become Sanyasis rather than beget children. Then Daksha had 1000 more sons, giving them the same instruction, but Narada similarly convinced them to become Sanyasis rather than beget children. Daksha was so angered that he put the following curse on Narada:
You have made me lose my sons once, and now you have again done the same inauspicious thing. Therefore you are a rascal who does not know how to behave toward others. You may travel all over the universe, but I curse you to have no residence anywhere.
And Narada voluntarily accepted the curse:
My dear King, since Nārada Muni is an approved saintly person, when cursed by Prajāpati Dakṣa he replied, “tad bāḍham: Yes, what you have said is good. I accept this curse.” He could have cursed Prajāpati Dakṣa in return, but because he is a tolerant and merciful sādhu, he took no action.
Not to keep you in suspense, Daksha ultimately fulfilled his responsibility as a Prajapati to populate the earth by having a bunch of daughters whom he married off to various gods and sages, as described in the next chapter of the Srimad Bhagavatam.
Bhagavatha Puranam Canto 6.5 describes how all the sons of Dakṣa were delivered from the clutches of the material energy by following the advice of Nārada, who was therefore cursed by Dakṣa. Influenced by the external energy of Lord Viṣhṇu, Prajāpati Dakṣa begot ten thousand sons in the womb of his wife, Pancajanī. These sons, who were all of the same character and mentality, were known as the Haryasvas. Ordered by their father to create more population, the Haryasvas went west to the place where the river Sindhu (now the Indus) meets the Arabian Sea. In those days this was the site of a holy lake named Narayaṇa-saras, where there were many saintly persons. The Haryasvas began practicing austerities, penances and meditation, which are the engagements of the highly exalted renounced order of life. However, when Srīla Narada Muni saw these boys engaged in such commendable austerities simply for material creation, he thought it better to release them from this tendency. Narada Muni described to the boys their ultimate goal of life and advised them not to become ordinary karmīs to beget children. Thus all the sons of Dakṣa became enlightened and left, never to return. Prajāpati Dakṣa, who was very sad at the loss of his sons, begot one thousand more sons in the womb of his wife, Pancajanī, and ordered them to increase progeny. These sons, who were named the Savalāśvas, also engaged in worshiping Lord Viṣhṇu to beget children, but Narada Muni convinced them to become mendicants and not beget children. Foiled twice in his attempts to increase population, Prajāpati Dakṣa became most angry at Narada Muni and cursed him, saying that in the future he would not be able to stay anywhere. Since Narada Muni, being fully qualified, was fixed in tolerance, he accepted Dakṣa’s curse.