Theory time :-)
(1.) My question is what things can you do to gain (or lose) favor?
A. A number of things, from tasks, all the way up to and including the favor required towards nobility.
(2.) what events will require favor?
A. Child contracts, marriage, service, employment, soldiering.
(3.) Completing tasks will increase favor but will all NPCs be willing to give you tasks?
A. I expect not all will give you tasks, but the tasks you perform may grant favor to groups rather than just individuals. A town hero sort of thing.
(4.) How about gifts? Can you throw money at NPCs to make them like you?
A. I expect yes, to a certain degree.
(5.) Is just saying hi every day enough to build favor?
A. There will probably be a repeated interaction buff to favor.
(6.) As for where favor is used you will need it to inherit from NPC parents. I assume it's required to form a child contract with an NPC but what else? Could you use this mechanic to convince NPCs to move to a new settlement or start converting NPC Brudvir to the Virtori and name them the Axe of the Virtues?
A. I know they said there was a mechanic for convincing tribes to move.