Thanks again for all the replies.
A few observations:
1) As Benta pointed out, the alternate pin sequence has to be used for diode in KiCAD.
2) SiliconWizard, yes, an additional resistor to the ground on the output part was planned to be added

3) inse, while the main issue was the diode polarity, there is indeed something to be understood concerning the operation mode of the current-feedback op amps. The main idea is to find the peak voltage of relatively short pulses (1us or so) of positive polarity with these op amps (which also have rather high slew rate).
The corrected schematics works as expected now, thanks. The evil was the diode pin assignment. Nevertheless, I see some cases of the input pulses, when I have to add one more diode right at the output of op amp in reverse direction, otherwise it does not seem to be be operational and saturates the whole thing to supply voltage right at the first pulse. I believe it has something to do with the op amp being of a current-feedback type. Please see the working example below (part of the schematics is shown with input and output oscillograms, since the whole thing is rather big). The non-working case is shown in the last two screenshots.