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

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

Without false ceiling you can use a good quality Silent decorative fan with LED directly - either as 3 lamps below or a single lamp shade. Select fan size & light as per the room area. Also using one or more big colorful pendant lamps (suiting your interiors) can light up the mood!

pendant lights looks nice only if place above a table like a breakfast nook or island. hanging them freely does not complement their look. since there is no island under the ceiling try to embed recessed lights in the ceiling. alternatively track lights will also look great if you need brightness.