You are right, the ADC should read around 512, and provided that you’ve connected the op.amp. correctly, the output voltage should be around 2.5 V.
My first immediate concern would be that you haven’t indicated what you’re doing with the second op.amp in the package. With no connections, it could be doing anything, so I’d suggest you connect it as a follower (exactly the same as the half you’re using, with the non-inverting input connected to the centre voltage, but leave the output connected only to the inverting input (not connected in parallel with the other – that is additionally connect pins 6 - 7 and 3 - 5).
The second concern is your use of a prototype board. The op.amp has a quite high gain-bandwidth product, and the prototype board with have a lot of stray capacitance everywhere. It’s quite possible that you have an oscillator - definitely something that’s not wanted. I’d suggest trying something like Fig. 48 on the data sheet. You’ll need to experiment with the value for CLOAD - I’d think in the range 0.1 µF to 1 µF should be adequate.
