Yes both measures fine in both directions, the ESR micro measures both esr and capacitance. I did measure all electrolytic caps, the 5 main caps seems fine and measures 0.3ohms and 203µF.
Two caps might be on the edge but I'm not completely sure, they measures 7.3ohms and 10.9µF in circuit - the datasheet does not list esr for the NFC series
That part may or may not be normal, I'll explain. ZD = Zener Diode. When testing Zeners with a multimeter in diode mode, if for example the testing voltage of your meter is 3V, and the diode is 2V (rated lower than your meter's testing voltage) then you'll get a reading in both directions, while the reading in the reverse direction would be higher than the other! However, if the diode is rated higher than your meter's voltage, then youre suppose to get a reading only in the correct polarity and not in the other. So to sum it up, you have to know the specs of the diode in order to determine if that's normal or not! Try looking at it with a magnifier and some light, if you can't get the model from that, then I'd advise you to desolder it so you could have a better look.
As for the caps though, it's possible that they're connected in series (and that youre getting a reading of both, and not just each standalone) not to mention there could be other things in the circuit negatively affecting the measurement. I'd say it'd be best you desolder em and test em again. As for their datasheet, if the esr/impedance isn't mentioned, then they're prob not low ESR (which is not surprising, as that's fairly rare for such low capacitance)