Assalaamu alaykum. If a person supplicates, "O Allah, facilitate for all of the people in the world to be Muslim," or, "O Allah, grant all of the poor wealth and success," what should their intention be? When we supplicate, we should hope that Allah will accept it. Therefore, with this type of supplication, what should be in the person's heart in terms of hope of in it being accepted? May Allah reward you.

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.

Supplicating Allah to guide all the people at all times is supplicating with what is impossible, because the Word of Allah has preceded in His speech in that He will fill Hell with jinn and people. Allah says (what means): {And if we had willed, We could have given every soul its guidance, but the Word from Me will come into effect [that] "I will surely fill Hell with jinn and people all together.} [Quran 32:13] 

Nevertheless, it is permissible to supplicate for the guidance of all people in a particular time, for example, as well as supplicating for them with wealth and success and so on.

Supplicating for wealth and success is like supplicating for guidance, so it is not permissible to supplicate with this supplication for all people at all times a general supplication, as it is a supplication for something impossible. The wisdom of Allah necessitated that there would be rich people and poor people.

Allah Says (what means): {Do they distribute the mercy of your Lord? It is We Who have apportioned among them their livelihood in the life of this world and have raised some of them above others in degrees [of rank] that they may make use of one another for service. But the mercy of your Lord is better than whatever they accumulate.} [Quran 43:32]

Allah also says (what means): {Look how We have favored [in provision] some of them over others. But the Hereafter is greater in degrees [of difference] and greater in distinction.} [Quran 17:21]

However, if he makes such a supplication for people of a specific time, for example, then it is permissible.

If the supplication is not Islamically prohibited, then when one supplicates, he should hope for the favor of Allah and that Allah answers his supplication. He should have good expectations of Allah and seek His favor and expect His vast mercy as His treasures are full and nothing can decrease them. Allah is Omnipotent and Capable of everything.

Having the intention of benefitting all the people and hoping that they would be guided and embrace Islam is something good that indicates the sincerity of the faith of the person and the goodness that is in his heart.

Allah knows best.