Yes it is feasible, to use the center tap connection on your transformer for lower output voltages. Actually a good idea....That way the heat dissipated by the regulator will be cut in half.
How to detect if it is in high range? Many ways to do this...but the simplest would be to add, in parallel with the input filter caps (C1, C2), a LED with its current limiting resistor, and a 16 volt zener in series. That way, in the low range, the voltage will not be enough to breakdown the zener +led voltages and it will be dark. In the high range, there will be sufficient voltage to light it up.