did they need to relay on others ?
I hope you can base your answer on the OT
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Some professions of OT prophets are recorded, but likely many of them were supported by God himself and by those putting faith in their message (much like Jesus would later be).
Did they have to rely on others?
Yes, but their need to rely on others was a test on those they were sent to. Ultimately their reliance was on God himself, and the perceived need of the prophet was a test on the people the prophet was sent to.
A very good example is Elijah in 1 Kings 17
At first God feeds Elijah through the ravens themselves, showing as in many cases in Elijah's life, God's ability to provide directly for the prophet.
Second a person is used to feed Elijah - and when they give the last of what they have, yet another miracle is given so that both are fed.
This is not very different than any other prophet situation, because everything under the heavens belongs to God. If anyone could provide food for a prophet, they are giving something that was first given to them, and could be rewarded based on that faith - just like the widow of Zarephath was.
To reiterate - in every case the prophet's needy state was simply a test on those he was sent to.
Were they poor or wealthy?
The majority of what we know about OT prophets is that they were generally not wealthy, and this was not by accident - the prophets represented people lightly esteemed by the world of that time. But there are a few who had prophetic roles, directly or indirectly, who were not exactly the poor either.
Moses: House of Pharoah (wealthy), turned Shepherd (not wealthy). While not necessarily poor, he was progressively humbled through is work to the point that he is called "The meekest on the earth". (Exodus 2)
Samuel Not necessarily rich or poor, but instead a dedicated prophet. If he had access to wealth (being in the service of the temple) there is nothing to suggest he made personal use it. A clue we have on his wealth-or-not priorities was that he generally always wore the little coat his mother made him, and not expensive attire he may have had access to - 1Sa 2:18, 19. He was also good in his dealings. 1 Samuel 12:4,5
Jeremiah Definitely not wealthy and did not benefit from the world at that time. His attendant was, however, and it proved to be somewhat of a snare to the attendant. The entire book of Jeremiah testifies to his lowliness - especially the statement recorded here: Jeremiah 45:5 - he could not have given such advice as a wealthy man.
Solomon A bit of a prophet through example, and definitely wealthy - but an example in wisdom and a prefiguration of Jesus in his kingdom. Later became unfaithful. Solomon is a common example of a wealthy man, and there are prophesies hidden scattered his writings in proverbs and Ecclesiastes.
Elijah Elijah, during the time of his prophesying, was far from wealthy - to the point that God fed him by having ravens carry him food, and later by a few miracles. Spent much of his time on the run. See above.
Amos Shepherd and fig farmer. Not wealthy professions. Amos 7:14
Daniel One of the foremost prophets with the most interesting books of OT, we could say that Daniel was likely wealthy in terms of position and power, and likely had the perks of his position available to him if he wished, but its obvious that was not his concern. He was definitely wealthy at Babylon's fall when they gave him gifts and promoted him. Daniel 5:29
Abraham Not necessarily known as a prophet, but certainly a tool of prophesy, was wealthy to a degree as many were dependent on him - but thats not an emphasis of his life. Genesis 24:35
Joseph Certainly a prophet - had a series of ups and downs in wealth. Ended up being a foremost ruler of Egypt. Genesis 41
Ezekiel The priesthood - but (wealthy profession?) was called to be a prophet, and the details of his prophesying work certainly do not reflect wealth at the time, but rather showed the poverty people would suffer in being reduced to eating food by careful ration cooked over dung cakes. Ezekiel 4:12
These are a few commonly known examples.
Poverty by Necessity
Prophets, during the time of their prophesying, rarely had "the good life" but were generally known for being treated insolently and being among the lower ranking ones of the world, much in the spirit of what is stated later in NT: 1 Corinthians 1:27 - God chose the foolish things of the world.
Depending on how you define wealth, you could even say they were the richest in the world, but again, proving such a thing requires New Testament reasoning provided by Christ, considering treasure in heaven.
If we assess a prophet according to their station during the time of their prophesying, most had very little.
Even Joseph, though quite wealthy in the end, was still at "prisoner" status when he arrived before Pharaoh to make the future known.
Although Daniel was indeed rich in comparison to his contemporaries, he longed to be back in Jerusalem, so likely the "riches" of the pagan empire were worthless in his eyes, keeping him poor in his own eyes.
Moses abandoned the rich life altogether. Its part of the OT story, but confirmed in the NT Hebrews 11:26-27 - summing up an important lesson.
You've asked a very good question, because the "wealth" of a prophet and their attitude toward their wealth (or lack of) is a very important part of their message, their values, and their faith.