With the inputs floating the gain is not unity. There is an infinite resistance between the \$470 \Omega\$ resistor and ground. The op-amp gain in the floating case is:
$$\underset{R_{i}\rightarrow\infty}{\lim}\frac{R_{f}}{R_{i}}=0$$
The thermal noise for the input resistor increases as \$\sqrt{R_{i}}\$ while the gain decreases as \$\frac{1}{R_{i}}\$. , so the noise is reduced as shown in the first graph. The input referred noise produced by the op-amp is amplified by the non inverting gain of the op-amp which is unity for floating inputs.
For the second case, the \$470 \Omega\$ resistors are grounded, so the thermal noise of the \$470 \Omega\$ is amplified by unity.
The input referred noise of the op-amp is multiplied by the non-inverting gain of 2. The total noise is the quadrature sum of the two.
The third case is the same as the second with a resistance of \$50+470=520\Omega\$.
The low frequency noise is called \$\frac{1}{f}\$ noise or flicker noise. It is characteristic of operational amplifiers, not ADCs. I am surprised at the reduction when the circuit is open circuit. I expected a 6dB reduction based on op-amp noise being amplified by non-inverting gain. Perhaps someone else in the community has an explanation.
How can it be that the measured noise is clearly dependent on the input circuitry of the op-amp driver, even though the noise is dominated by the ADC?
The noise is based on the op-amp and its circuit not the ADC. Certainly the ADC and circuit layout contribute. The datasheet (Page 37) for the amplifier clearly outlines all the noise sources and the effect of the gain components on the noise. I suggest reading this carefully and completely. Some other articles are:
