From what I know much of the detail have yet to be released however if you join a family that runs or operates some sort of a business then you get a small bonus to learning and advancing in the family business. If your father is a blacksmith then you get a small bonus to learning blacksmithing and he can also train you at home without you having to seek out a trainer.

Each character (either NPC or Player Character) will have a personality and will do what ever is in their individual interest. I would think if your father barely has enough work to keep the family fed then the children may look for work outside the home. If a farmer is doing well I would think most of the children would stay at home and help. Now about running a shop I am not sure about but I would assume the same would be valid if a 'merchant' was the particular profession of the parents.

And finally 'animal breeding' will take some DNA into effect when breeding. From attempting to domesticate, tame, or breed for purpose, there will be more to it than just placing two animals together and poof, an offspring, some planning needs to be considered. There will be also bee breeding if are so inclined to try your hand at a smaller critter.

I'd say if you have a big enough family, I don't see why not. However, in the early years of business, you'll probably have to hire randos. Unless you start with a relatively big family.

I had a little bit of discussion about breeding early on in 2015. It looks like the potential is there. It was one of the things that drew me into this game idea. Same thing with farming to create new or better crops and building materials... since one of the core aspects of its development was research and technology development I take that to mean you should be able to do it.

Should be easy enough to start a business and get your family involved

Honestly I hope so. Gonna try being a merchant in the game and in the early days I would love to work with family businesses