SDO/HMI and SDO/AIA data for the 24th solar-activity cycle are analyzed using a quicker and more accurate method for resolving π ambiguities in the transverse component of the photospheric magnetic field, yielding new results and confirming some earlier results on the magnetic properties of leading and following magnetically connected spots and single spots. The minimum inclination of the field lines to the positive normal to the solar surface α min within umbrae is smaller in leading than in following spots in 78% of the spot pairs considered; the same trend is found for the mean angle 〈α〉 in 83% of the spot pairs. Positive correlations between the α min values and the 〈α〉 values in leading and following spots are also found. On average, in umbrae, the mean values of 〈B〉, the umbra area S, and the angles α min and 〈α〉 decrease with growth in the maximum magnetic field B max in both leading and following spots. The presence of a positive correlation between B max and S is confirmed, and a positive correlation between 〈B〉 and S in leading and following spots has been found. Themagnetic properties of the umbrae of magnetically connected pairs of spots are compared with the contrast of the He II 304 emission above the umbrae, C 304. Spots satisfying certain conditions display a positive correlation between C 304−L and 〈α L 〉 for the leading (L) spots, and between C 304−L /C 304−F and l L /l F , where l L (l F ) are the lengths of the field lines connecting leading (L) or following (F) spots from the corresponding spot umbrae to the apex of the field line.