Scarce longitudinal evidence examines LLMs' persuasiveness and humanness along time-evolving psychological frameworks. We introduce Talk2AI, a longitudinal framework quantifying psycho-social, reasoning and affective dimensions of LLMs' persuasiveness about polarizing societal topics. In a four-way longitudinal setup, Talk2AI's 770 participants engaged in structured conversations with one of four leading LLMs on topics like climate change, social media misinformation, and math anxiety. This produced 3,080 conversations over 60,000 turns. After each wave, participants reported conviction in their initial topic stance, perceived opinion change, LLM's perceived humanness, a self-donation to the topic and a textual explanation. Feedback time series showed longitudinal inertia in convictions, indicating some human anchoring to initial opinions even after repeated exposure to AI-generated arguments. Interestingly, NLP analyses revealed that both humans and LLMs relied on fallacious reasoning in 1 conversational quip every 6, countering the ``LLMs as superior systems" stereotype behind LLMs' cognitive surrender. LLMs' perceived humanness was most learnable from sociodemographic, psychological and engagement features ($R^2=0.44$), followed by opinion change ($R^2=0.34$), conviction ($R^2=0.26$) and personal endowment ($R^2=0.24$). Crucially, explainable AI (XAI) indicated: (i) the presence of individuals more susceptible to LLM-based opinion changes; (ii) psychological susceptibility to LLM-convincing consisted of having more trust in LLMs, being more agreeable and extraverted and with a higher need for cognition. A multiverse approach with mixed-effects models confirmed XAI results, alongside strong individual differences. Talk2AI provides a grounded framework and evidence for detecting how GenAI can influence human opinions via multiple psycho-social pathways in AI-human digital platforms.