The next mission dedicated to the study of planetary atmospheres is the Ariel space mission, planned for launch in 2029, which will observe a variety of planetary systems belonging to different classes around stars with spectral types from M to A. To optimise the scientific outcome of the mission, such stars need to be homogeneously characterised beforehand. In this work, we focus on a methodology based on spectral synthesis for the characterisation of FGK-type stars from the Ariel Tier 1 Mission candidate sample (MCS) which exhibit fast rotation. In addition, we analyse 108 slow-rotating FGK-type stars, with either new observations or archival spectra available, consistently as in our previous work using the equivalent width (EW) analysis. Using our homogeneous set of stellar parameters, we studied the correlations between stellar and planetary properties for the Ariel MCS analysed so far. We confirmed a close relationship between stellar mass (up to 1.8 Msun) and giant planet radius, with more inflated planets at lower metallicity. We confirm that giant planets are more frequent around more metal-rich stars that belong to the thin disc, while lower-mass planets are also found in more metal-poor environments, and are more frequent than giant planets in the thick disc as also seen in other works in the literature.