my houses only stay in my home system.

You can give them as many systems as you have - there's no detriment to you.

The more I think about it, the more the mechanic makes sense of how the houses are happy for a time and always get mad and demand more territory. Kind of forces a Klingon player to always expand. I think there was a quote (DS9 maybe?) about how the Klingons always had to expand or die.

On the other questions, I'm not a dev (I'd like one to weigh in with more detail) but here's what I've seen so far:

-You can't see what houses have what systems. You just have to remember. It doesn't matter really. The house will eventually start producing ships there if they have enough materials.

-The bigger the house, the more territories to give them. Just try to keep the biggest ones as happy as possible and don't worry about the little ones until they expand and become a significant portion of the population. Inhabited planetary systems seem to quench their thirst better than others.

-I thought it might create a sector too but it doesn't. It's just a system for them to "own" and protect that affects their happiness. I'm guessing inhabited systems give them more resources to build ships and as I said above, seem to go farther to making them temporarily happy.

-I haven't been able to direct house fleets in peacetime. I tried to have them rally on my fleet to go fight some pirates and they wouldn't follow. Hopefully it works differently in wartime so they're not just throwing themselves at starbases and losing. If nothing else, they'd act as defense fleets if you're invaded.

It would be kewl if the Great Houses replaced vanilla sectors.