If you loot or buy the following tokens from the broker, you can speed up your faction gain. If you buy them, make sure they are from one of the two factions you are not trying to increase faction with before you turn them in to, since all three are opposed to each other.
In order to buy each type of residence (by size), the specific the residency licenses in the table below are required. This means that buying the most expensive (Affluent Maj'Dul residency license will not give you the freedom to buy the other two house types.
It is not required to upgrade to the larger homes, because each type (small, medium, and large) requires a separate licence.