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

Pendants seem like a better geometric fit.

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

Suraj, If you have access to the room that you shared earlier you can try seeing the flicker effect at night time with both lights and fan being on. If the lamp has a 360 degree light spread it will cast the fans shadow on the ceiling and when the fan is turned on it causes a flikr effect. I personally find it a distraction and at the same time many would not even notice it. Take the pick based on your usage. Wall mounted fans and recessed fans can also be explored. Thanks, Nitin Cornerstone Designs, Bangalore.