Aims. Our aim in this paper is to refine the orbital and physical parameters of the HATS-2 planetary system and study transit timing variations and atmospheric composition thanks to transit observations that span more than 10 yr and that were collected using different instruments and pass-band filters. We also investigate the orbital alignment of the system by studying the anomalies in the transit light curves induced by starspots on the photosphere of the parent star. Methods. We analysed new transit events from both ground-based telescopes and NASA's TESS mission. Anomalies were detected in most of the light curves and modelled as starspots occulted by the planet during transit events. We fitted the clean and symmetric light curves with the JKTEBOP code and those affected by anomalies with the PRISM+GEMC codes to simultaneously model the photometric parameters of the transits and the position, size, and contrast of each starspot. Results. We found consistency between the values we found for the physical and orbital parameters and those from the discovery paper and ATLAS9 stellar atmospherical models. We identified different sets of consecutive starspot-crossing events that temporally occurred in less than five days. Under the hypothesis that we are dealing with the same starspots, occulted twice by the planet during two consecutive transits, we estimated the rotational period of the parent star and, in turn the projected and the true orbital obliquity of the planet. We find that the system is well aligned. We identified the possible presence of transit timing variations in the system, which can be caused by tidal orbital decay, and we derived a low-resolution transmission spectrum. C1 [Biagiotti, F.] Univ Roma La Sapienza, Dept Phys, Pl Aldo Moro 2, I-00185 Rome, Italy. [Biagiotti, F.] Via Fosso Cavaliere 100, I-00133 Rome, Italy. [Mancini, L.; Naponiello, L.; Basilicata, M.] Univ Roma Tor Vergata, Dept Phys, Via Ric Sci 1, I-00133 Rome, Italy. [Mancini, L.; Naponiello, L.; Basilicata, M.] via Osservatorio 20, I-10025 Pino Torinese, Italy. [Mancini, L.; Henning, Th.] Max Planck Inst Astron, Konigstuhl 17, D-69117 Heidelberg, Germany. [Southworth, J.] Keele Univ, Astrophys Grp, Keele ST5 5BG, England. [Tregloan-Reed, J.] Univ Atacama, Inst Astron & Ciencias Planetarias Atacama, Copayapu 485, Copiapo, Chile. [Naponiello, L.] Univ Florence, Dept Phys & Astron, Largo Enr Fermi 5, I-50125 Florence, Italy. [Jorgensen, U. G.; Bach-Moller, N.] Univ Copenhagen, Niels Bohr Inst, Ctr ExoLife Sci, Oster Voldgade 5, DK-1350 Copenhagen, Denmark. [Bonavita, M.; Snodgrass, C.] Univ Edinburgh, Inst Astron, Royal Observ, Edinburgh EH9 3HJ, Scotland. [Bozza, V.] Univ Salerno, Dept Phys ER Caianiello, Via Giovanni Paolo II 132, I-84084 Fisciano, Italy. [Bozza, V.] Ist Nazl Fis Nucl, Sez Napoli, Naples, Italy. [Burgdorf, M. J.] Univ Hamburg, Meteorol Inst, Dept Earth Sci, Bundesstr 55, D-20146 Hamburg, Germany. [Dominik, M.; Jaimes, R. Figuera] Univ St Andrews, Ctr Exoplanet Sci, Sch Phys & Astron, SUPA, North Haugh, St Andrews KY16 9SS, Scotland. [Jaimes, R. Figuera] Millennium Inst Astrophys MAS, Nuncio Monsenor Sotero Sanz 100,104, Santiago, Providencia, Chile. [Jaimes, R. Figuera] Pontificia Univ Catolica Chile, Inst Astrofis, Av Vicuna Mackenna 4860, Santiago 7820436, Macul, Chile. [Hinse, T. C.] Univ Southern Denmark, Dept Phys Chem & Pharm, Campusvej 55, DK-5230 Odense M, Denmark. [Hundertmark, M.] Zentrum Astron Univ Heidelberg ZAH, Astron Rechen Inst, D-69120 Heidelberg, Germany. [Khalouei, E.; Rahvar, S.] Seoul Natl Univ, Res Inst Basic Sci, Astron Res Ctr, 1 Gwanak ro, Seoul 08826, South Korea. [Longa-Pena, P.] Univ Antofagasta, Ctr Astron, Av Angamos 601, Antofagasta, Chile. [Peixinho, N.; Rabus, M.] Univ Catolica Santisima Concepcion, Fac Ingn, Dept Matemat & Fis Aplicadas, Alonso Rivera 2850, Concepcion, Chile. [Sajadian, S.] Isfahan Univ Technol, Dept Phys, Esfahan 8415683111, Iran. [Skottfelt, J.] Open Univ, Ctr Elect Imaging, Dept Phys Sci, Milton Keynes MK7 6AA, England. [Jongen, Y.] Pres Ctr Equestre Palis, Observ Vaison La Romaine, Dept 51, F-84110 Vaison La Romaine, France. [Vignes, J. -p] KNC Deep Sky Chile Observ, Santiago, Chile. C3 Sapienza University Rome; University of Rome Tor Vergata; Max Planck Society; Keele University; Universidad de Atacama; University of Florence; University of Copenhagen; Niels Bohr Institute; University of Edinburgh; University of Salerno; Istituto Nazionale di Fisica Nucleare (INFN); University of Hamburg; University of St Andrews; Pontificia Universidad Catolica de Chile; University of Southern Denmark; Ruprecht Karls University Heidelberg; Seoul National University (SNU); Universidad de Antofagasta; Universidad Catolica de la Santisima Concepcion; Isfahan University of Technology; Open University - UK