RFID reader antenna with 2 series capacitors - what do they stand for?
If I look carefully at the photos of the HZ-1050 it appears to have at least one 3.3 nF capacitor already. Also I see that the antenna that is used does not have any capacitors. Maybe your antenna coil has a higher inductance than most antennas and it needs 2 3.3 nF caps in series. If you can try shorting one of the caps on the antenna and see if that helps. If not, try shorting both. You could also short the capacitor on the PCB but make sure there is at least one capacitor in series with the antenna coil at all times. It does not matter if the capacitor is on the PCB or in the antenna as long as there is a cap.

1) The caps make a series resonant circuit in combination with the antenna coil. It seems they needed 1.65 nF which is two 3.3nF in series.

2) There's also a cap on the board and now there are too many caps making the system oscillate at the wrong (too high probably) frequency.

3) see above