The HQ magnet is a 120 mm aperture, 1-meter-long Nb3Sn quadrupole developed by the LARP collaboration in the framework of the High-Luminosity LHC project. A first series of coils was assembled and tested in 5 assemblies of the HQ01 series. The HQ01e model achieved a maximum gradient of 170 T/m at 4.5 K at LBNL in 2010-2011 and reached 184 T/m at 1.9 K at CERN in 2012. A new series of coils incorporating major design changes was fabricated for the HQ02 series. The first model, HQ02a, was tested at Fermilab where it reached 98% of the short sample limit at 4.5 K with a gradient of 182 T/m in 2013. However, the full training of the coils at 1.9 K could not be performed due to a current limit of 15 kA. Following this test, the azimuthal coil pre-load was increased by about 30 MPa and an additional current lead was installed at the electrical center of the magnet for quench protection studies. The test name of this magnet changed to HQ02b. In 2014, HQ02b was then shipped to CERN as the first opportunity for full training at 1.9 K. In this paper, we present a comprehensive summary of the HQ02 test results including: magnet training at 1.9 K with increased pre-load, quench origin and propagation, and ramp rate dependence. A series of powering tests was also performed to assess changes in magnet performance with a gradual increase of the MIITs. We also present the results of quench protection studies using different setting for detection, heater coverage, energy extraction and the Coupling-Loss Induced Quench (CLIQ) system. However, the full training of the coils at 1.9 K could not be performed due to a current limit of 15 kA. Following this test, the azimuthal coil pre-load was increased by about 30 MPa and an additional current lead was installed at the electrical center of the magnet for quench protection studies. The test name of this magnet changed to HQ02b. In 2014, HQ02b was then shipped to CERN as the first opportunity for full training at 1.9 K. In this paper, we present a comprehensive summary of the HQ02 test results including: magnet training at 1.9 K with increased preload, quench origin and propagation, and ramp rate dependence. A series of powering tests was also performed to assess changes in magnet performance with a gradual increase of the MIITs. We also present the results of quench protection studies using different setting for detection, heater coverage, energy extraction and the Coupling-Loss Induced Quench (CLIQ) system.