Postive input ==> Positive and Negative output
Yes, you connect the output of the divider to the input of the opamp. If you would use the output of the divider directly the voltage would vary depending on what load you connect to it. With the opamp you have a high impedance load, meaning that there doesn't flow any current into the opamp and the voltage on its input will remain at Vin/2.
The opamp will set its output so that both inputs are equal, so for the voltage follower this means that the output voltage is equal to the input voltage. The opamp can supply some current (not much really) and a small load won't change the Vin/2 at the output.
I'm not sure I understand your last question.