What are they doing?
How do they sustain themselves?
Trade is the Hlaalu’s primary source of income. Their primary trade has historically been exports and imports to and from foreign lands, even as intermediaries to other houses. They had a less well-established role in internal trade (as the Indoril were trying to occupy that position when trade between houses was not done directly), but it did exist; the recent Hlaalu landgrabs are an attempt to increase their control of internal trade.
Historically, the inferior position of Hlaalu in terms of regulating internal trade pushed them towards involvement in markets the Indoril were not willing to involve themselves in; secret trades that went on during house wars out of sight, and then later involvement in the criminal underworld.
After trade, plantations, farms, ranches, and kwama mines are used both for local consumption and export, as are the newer and more rare ore mines. As a governing faction, they also raise money through taxation, and likely profit from housing many Imperial factions and administrative bodies.
Notable is their high level of slave trade and production of alcohol. In the Othreleth Woods (and Shipal Shin) in particular should be regional liquor flavors, distilleries and wineries.
Finally, the House (or parts of the House) are engaged in criminal activities (notably drug trade) and corruption, which also fills coffers.
What is common knowledge about them?
They are traders.
Alternatively, for Dunmer, they are corrupt greedy merchants who are in bed with the Empire. They have a reputation for adopting outlander culture and abandoning or ignoring a lot of Dunmer culture. Disloyal backstabbers. In bed with crime.
For the Empire, they are friendly towards outlanders and relatively enlightened and relatable, they can always be reasoned with, but never fully trusted as they are cut-throat merchants at best and swindlers at worst.
For Imperials outside of Morrowind, the Hlaalu are merely another merchant company, similar to merchant-aristocrats like the Briricca.
What do members know about their faction that outsiders don't?
Since the Hlaalu are fairly easy to join as hirelings, it consequently means that the information for the rank and file is rather limited.
Generally, members get insider knowledge on things like local trades and trade routes, what authorities can be dealt with in what ways (i.e. bribery, blackmail); some might know information about criminal activities.
What dirty secrets do the in-the-know people know?
In general, the higher ranking members would know how the connection between House Hlaalu and the Camonna Tong works. Alongside this, they would naturally have an overview over trade routes, administration of lands, money flow.
The “normal” upper levels of the House would understand how the actual dynamic between the Empire and the Hlaalu works: the Hlaalu understand the Empire as an overbearing trade partner that can be swindled, but not ignored, while the Empire in turn is trying to manipulate the Hlaalu to its advantage and is not aware of the depth of Hlaalu operations.
Limited to the Council Electors is knowledge about a long-term plan of survival.
The plan was originally hatched during the Tiber Wars, as the eastern houses stated their unwillingness to defend western Morrowind (favouring guerilla tactics in the interior of the province), and Hlaalu and Redoran were faced with the prospect of having their lands overrun without outside support.
While most Hlaalu advocated appeasement, and while Redoran were preparing for defeat in battle, the councillors were forced to consider all of the worst-case scenarios that faced them and try and find a path for survival, to an extent of themselves, to an extent of their house, and to an extent of Morrowind as a whole.
As it turned out, Vivec saved them from the worst by signing the Armistice, effectively putting Morrowind under Imperial control while maintaining a large degree of autonomy for the houses and Temple. The survival of the house was assured for the moment, but nobody was sure how long the situation would last.
With Indoril and Redoran internally weakened as a result and the Empire poised to set up shop in Morrowind, the Hlaalu were suddenly in a strong position to expand their power and diversify from being pass-bound merchant clans to possessing a strong economy, infrastructure, territory and political position. By doing so, they could ensure that their survival would not be as easily threatened in future.
However, there were still powerful factions that could threaten House Hlaalu. For one, the other houses, the strongest of which was still House Indoril. For another, the Empire. While Hlaalu set about taking what land they could from Redoran and Indoril, they did not forget about the potential threat the Empire or its eventual absence presented to them, and considered ways to survive in all possible outcomes.
Their answer was to keep the Empire close, encourage involvement with it on all levels within the house, adopt the new ideas it brought with it where they could use them to their advantages, form strong bonds with local officials, thereby avoiding those officials feeling a need to establish a strong military presence in Hlaalu lands.
In short, the Hlaalu intertwined themselves with the Empire, but the councillors never stopped having and updating an exit plan in case it would one day no longer prove advantageous or possible to remain under the Empire’s mantle. What that exit plan was and when it should be enacted, however, would prove to be a source of continuing disagreement, which would lead to delicate situations during events such as the War of the Red Diamond, the failed invasion of Akavir, and more recently the Simulacrum.