What is known as far as: Their Purpose, Their Direction, What was their Military Level (Ie, if today Knights still fought, would the Knights Templar be known as Special Forces?) , Their Wealth level, etc. If you have insight as to this, i would love to know it. They Fascinate me, much like Sparta; Except Sparta's Society wasn't that secret.
We actually know quite a lot about the Templars, especially around the age of the Crusades and the few centuries after their founding. I'll address as many of your points as I can.
Their Purpose: The initially stated purpose of the Knights Templar was to serve as an order of monastic knights that would protect pilgrims on the road to Jerusalem. By the time of their foundation in the 12th century, European Crusaders held large chunks of territory in Syria and Palestine, but they remained surrounded by Muslim states with whom they were often at least in a state of hostility toward, if not outright war. Additionally there was consistent trouble on the road even in the Crusader-controlled Latin States, as much of the Muslim population that had lived there before their invasion remained. At that point there were exactly 9 knights in total, so they were useful for little else.
That would change rapidly. They were given territory close to what was believed to be Solomon's Temple, hence the Holy Order of the Temple of Jerusalem, aka the Order of the Knights Templar or just the Knights Templar. To quote Jonathan Riley-Smith on the order's growth:
the Templars gained the immediate support of the king of Jerusalem and the backing of leading members of the west European nobility ... The Templar way of life proved itself to be very attractive to contemporary nobles and knights.
They saw a lot of enrollment in their ranks shortly after their founding, and also had a lot of land donated to them by European lords in Europe. So they had income coming from land holdings in Europe on top of cash donations, holdings in the Holy Land, and the banking service they would eventually establish. The Order quickly developed from 9 knights guarding pilgrims on the road to a full-fledged monastic military. At the height of its power, when the order took the field it could muster hundreds and even thousands of knights and turcopoles and tens of thousands of common footmen. When they reached that stage, they were one of the largest military forces among the Crusader factions, and their cooperation was necessary if any Crusading endeavour could hope to be successful.
Their Direction: The Templars had an internal chain of command that would be readily recognizable as a military one, with serjeants answerable to knights answerable to a Grand Master. Ultimately, however, the vows of the Templars were sworn to the Pope, and to be a Templar was to be answerable to the church. They did not swear allegiance to the king (or queen) or Jerusalem, but it was uncommon for the Order to resist their plans and activities in a significant way.
Military Level: Knights are knights. There was nothing in terms of training or resources to necessarily set Templar knights apart from any of the other knights who found themselves in the Holy Land, so in that capacity at least they would not qualify as what we consider special forces. An argument could hypothetically be made for the footmen of the Templars to be superior over the normal rabble, as they did live lives of monastic discipline and were undoubtedly savvy veterans in battle, but making value claims would be speculative, IMO. They might be compared, however, to U.S. Army Rangers in terms of their implementation. As one of the powerful military bodies in the Latin States, the Templar forces would often be employed as the hammer of an assault.
Wealth Level: Rich, son. The Templars were in many ways the it charity, and as I mentioned before, they received a lot of donations - enough to establish their own proto-banking system so that pilgrims and other lords coming to the Holy Land could use their money without having to physically bring all of their money. They experienced highs and lows, of course, but by and large they were the most financially secure of the Crusaders' military orders. I should note, however, that that applies only to the institution. The men themselves swore vows of poverty, and while naturally there was a degree of corruption, we do know that soldiers received only a modest allowance to spend on themselves - after all, they had as many as 20 000 fighting men to house, feed, clothe, and arm, not to mention the chaplains, servants, and other affiliated personnel who didn't fight and had to mind the Templars' many holdings.
I hope this helps for some background. The Templars are really not nearly as mysterious as they're often made out to be, particularly when they were most relevant, so if you have any other questions or want more detail on any of this stuff, feel free to ask follow-ups.
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I'd like to add to /u/The1Man post that in no way the Templar order was "secret" during its times.
It was one of a number o chivalric orders that were born during the crusades, some of which still exist.
The order suppression was particularly brutal, and a they were the target of a propaganda campaign by the authorities doing the suppression (that is, the french monarchy).
A bunch of legends were attached to them after they ceased to exist, and a number of organizations, some of them born hundreds of years after, claimed to be descendants of the order as a way to gain more prestige.