Why do Muslims invite non-Muslims to Islam, even though leaving them and not inviting them might be better for them, given that they are in the category of "Ahl al-Fatra" who will be tested on the Day of Judgment? And is Hellfire prepared only for disobedient Muslims and Paradise for obedient Muslims, while non-Muslims who have not received the message of Islam are excused?

We, as Muslims, invite others to believe in Allah and His messengers, to do good, and to shun evil. This is in compliance with Allah's command and in emulation of the prophets who came to guide humanity. This is a communal obligation (fard kifayah) upon the Ummah and an individual obligation (fard ayn) upon each person according to their capacity and knowledge. Da'wah (inviting to Islam) contains great good for both the inviter and the invited, and Allah has saved many from disbelief because of it.

Therefore, the statement that not inviting them is better is incorrect. The fact that they will be tested on the Day of Judgment does not mean it is better for them, because whoever believes then is someone who would have believed in this world. And there is no excuse for anyone who heard about the Prophet Muhammad, peace be upon him, and did not believe in him.

As for your question: Are Hellfire and Paradise prepared for disbelievers and the righteous, respectively? That is a known necessity of the religion. Hellfire has been prepared for the disbelievers, and Paradise for the righteous.