Building more culture buildings does increase the spread of your culture/influence.
They might be force-targetting your cap ship instead of letting the ships pick their own targets (frigates tend to automatically attack other small ships, vis a vis with cap ships).
Matter of preference. Stick with the small, or smaller medium scenario maps.
Not sure about that one, sorry. I would guess it only gives you the perks (no culture bonus), but again, see previous sentance.
Also, you might want to avoid quadrouple-posting in the future. *hands you a fire extinguisher* You might need this in the near future.