1/ not at all, as long as there is connection life is good
2/ The proper terms are BFC (Big Fat Cross) (20 squares) and city's cultural borders (depending on cultural value of the city). Is that what you're talking about?
3/ It is
4/ This is the city's cultural borders. They grow as your city gets culture, at 10 (becomes the BFC), 100, 500, 5000 and 50000 culture at normal speed if I'm correct. The shaps remains approximately the same
5/ as long as a tile is inside the BFC of a city, you can work it in that city and thus gain food/commerce/hammers, regarding of the presence of improvements (you can take a look at the "finally ready for noble" game into the succesion games subforum for that
). But it will yeld better output with improvements obv. Exceptions are peaks, and water tiles if you don't have fishing.
6/ If a tile is inside the BFC of two cities at the same time, only one can work it. But you can choose. Just go into the city screen of one city and click on it.
7/ See before
8/ Basically, when a city is at size 1, it needs 22 food to grow to size 2. When it does, there is no food abymore into the food bar, except left-over.
If you have a granary, the food bar is filled with half of this. So in the present situation, you would have 11 food + left-over into the food bar when you grow to size 2.
9/ No problem