1 - You don't play a family, you play as the nation they live in (and to some extent its ruler character). The game won't end if ruling family dies out or changes. The closest you have is monarchies where you have one ruling family.
The ruling family is just like other families, except that one of their members happens to hold highest offices of the state. So yes, you'll get to see them from the same family list.
Because family members share a surname/middle name, you can identify them fast from that too. Though I do think adding a little graphic (something better than a blood drop) for immediate relatives of the ruler might be good.
2 - They should be, I think. There will most likely be a positive relationship modifier between members of the same family, just like older Paradox games. Family members tend to share the same goals often as well, so they would be more loyal to each other in politics. In EU-Rome two members of the Julii for example would join same faction in the Roman republic. They should do the same in here as well.
Also, even in monarchies this game will likely not have a medieval style system of claims and claimants, so yes, brothers and uncles will be loyal too.
3 - Families don't have relationships with each other so far, their members do. Such feature may exist in future I assume, either having not been revealed yet or in future DLCs.
You can make the individual characters of that family like the ruler character, however (remember, YOU are not playing a family - their relationship is with the ruler + the nation which you play). Bribing them, fostering friendships through events, fulfilling their ambitions and wishes, and giving them a chance at political or military career, all make them more loyal to the ruler character.
4 - You can marry two characters manually if you wish. Not sure if matrilinial has been added as a feature. In EU-Rome it was always father's family, so I guess wait for DLCs and patches or mods.
