About your opamp and resistor bias circuit: the resistors will indeed consume only little current; however, the opamp will need to regulate its output to continue to output 3.5V, regardless of its output loading. The only way it can do that, is draw from the 12V supply; so the opamp will behave effectively like a pass through transistor, dissipating the difference between 12V and 3.5V. If you want to be sure what current flows where exactly, you can take some opamp circuit spice model from a vendor's website and perform some spice simulations. This may be very insightful.
About your second question: I am not sure what you mean exactly, but at least the following should hold: the power is constant; so with higher voltage, less current will be available. Maybe this helps a little already.