Testing humanoid robots with users is slow, causes wear, and limits iteration and diversity. Yet screening agents must master conversational timing, prosody, backchannels, and what to attend to in faces and speech for Depression and PTSD. Most simulators omit policy learning with nonverbal dynamics; many controllers chase task accuracy while underweighting trust, pacing, and rapport. We virtualise the humanoid as a conversational agent to train without hardware burden. Our agent-centred, simulation-first pipeline turns interview data into 276 Unreal Engine MetaHuman patients with synchronised speech, gaze/face, and head-torso poses, plus PHQ-8 and PCL-C flows. A perception-fusion-policy loop decides what and when to speak, when to backchannel, and how to avoid interruptions, under a safety shield. Training uses counterfactual replay (bounded nonverbal perturbations) and an uncertainty-aware turn manager that probes to reduce diagnostic ambiguity. Results are simulation-only; the humanoid is the transfer target. In comparing three controllers, a custom TD3 (Twin Delayed DDPG) outperformed PPO and CEM, achieving near-ceiling coverage with steadier pace at comparable rewards. Decision-quality analyses show negligible turn overlap, aligned cut timing, fewer clarification prompts, and shorter waits. Performance stays stable under modality dropout and a renderer swap, and rankings hold on a held-out patient split. Contributions: (1) an agent-centred simulator that turns interviews into 276 interactive patients with bounded nonverbal counterfactuals; (2) a safe learning loop that treats timing and rapport as first-class control variables; (3) a comparative study (TD3 vs PPO/CEM) with clear gains in completeness and social timing; and (4) ablations and robustness analyses explaining the gains and enabling clinician-supervised humanoid pilots.