I have the following circuit:
I think I understand pretty much all the aspects of it except for the small capacitor in the feedback. What is the need for it? Judging by the frequency of 1 MHz that is the inverse product of the capacitance and the resistance, I can guess the need for this capacitor arises at high frequencies, when the gain of the amplifier tends to unity. However, I can't figure out the purpose.
The input capacitance of this opamp is a few pF which, combined with the rather high value feedback resistor, creates a pole at a frequency that's low enough to add enough phase shift in the feedback to reduce phase margin. This may make the opamp unstable or marginally stable.
The 10pF cap compensates for this. If you draw the opamp's input capacitance on the schematic, for example 2pF to ground on the "-" input, then it becomes clear how the 10pF cap forms a capacitive divider with this parasitic cap and restores phase margin.
Note the input capacitance is the parasitic capacitance of the input transistors, protection diodes etc, in the chip itself.