Yes, ideally the fan should be centered in geometric center of room, but when push comes to shove it absolutely needs not be of couse, but i think a ceiling fan that is not centered and a chandelier that is centered will not look good

Hope is patience with lamp lit !

Hello there, Since you have put an all white kitchen with recessed lighting, you won't be needing much lumens for the island. As for the length, two small pendants with 12/15W lamps spaced 2-3' apart would be enough to illuminate the space. It's always better than one large pendant because it disperses light over a larger area and aesthetically pleasing as well. Regards, Aurum Ideas and Spaces India

hi karen! do you have any photos of the dining and living room? would love to help, but photos might aid in an accurate suggestion