Gist
The calves stabilise the ankle and help control forward knee travel, but front squats alone rarely provide enough plantar-flexion loading for maximal calf growth.
The hamstrings assist and stabilise, but front squats are not a primary hamstring-building exercise because knee and hip motion limit their net shortening.
Yes. Front squats are an effective quadriceps exercise because the upright torso and knee travel create substantial knee-extension demand.
Yes. Front squats can build the glutes when depth, effort and loading progress, although the front-rack position often limits the load before the hips do.
Yes, chiefly through bracing. Holding the load in front increases the demand to resist trunk flexion, although the stimulus remains mostly isometric.