Is living in Makkah and praying most prayers in the Sacred Mosque (Haram) more rewarding than leading prayers as an Imam in a mosque outside the Sacred Mosque, such as in Jeddah, and is conveying the message of Islam (Da’wah) better than all of that?

The scholars have not explicitly stated a preference between inviting people to Allah (Da'wah), leading people in prayer (Imamah) outside Mecca, and performing congregational prayers in Mecca. It is better to combine them since there is no contradiction.

Inviting people to Allah is a great deed and does not contradict leading prayers or performing them. Mecca, with its honor, needs Da'wah even more, due to the multiplication of reward and sin within it, and the need of pilgrims (Hujjaj) and Umrah performers for education.

As for preferring between leading people in prayer outside Mecca and residing and praying there, each has its advantages. Leading prayers has its virtue and reward, but it is disliked by some scholars due to its guarantee and responsibility. Similarly, residing in Mecca is disliked by some of them due to the multiplication of misdeeds.

The preference between these two actions depends on individuals, circumstances, qualification for Imamah, and the needs of the people. A virtuous action for one person might be less virtuous for another, and a less virtuous action might be preferred for a person if it is more beneficial or easier for them.