[abridged] We analyse four transits of WASP-33b observed with the optical high-resolution HARPS-N spectrograph to confirm its nodal precession, study its atmosphere and investigate the presence of star-planet interactions.We extract the mean line profiles of the spectra by using the LSD method, and analyse the Doppler shadow and the RVs. We also derive the transmission spectrum of the planet, correcting it for the stellar contamination due to rotation, CLV and pulsations. We confirm the previously discovered nodal precession of WASP-33b, almost doubling the time coverage of the inclination and projected spin-orbit angle variation. We find that the projected obliquity reached a minimum in 2011 and use this constraint to derive the geometry of the system, in particular its obliquity at that epoch ($epsilon=113.99^{circ}pm 0.22^{circ}$) and the inclination of the stellar spin axis ($i_{rm s}=90.11^{circ}pm 0.12^{circ}$), as well as the gravitational quadrupole moment of the star $J_2=(6.73pm 0.22)times 10^{-5}$. We present detections of H$alpha$ and H$beta$ absorption in the atmosphere of the planet with a contrast almost twice smaller than previously detected in the literature. We also find evidence for the presence of a pre-transit signal, which repeats in all four analysed transits. The most likely explanation lies in a possible excitation of a stellar pulsation mode by the presence of the planetary companion. Future common analysis of all available datasets in the literature will help shedding light on the possibility that the observed Balmer lines transit depth variations are related to stellar activity and/or pulsation, and to set constraints on the energetics possibly driving atmospheric escape. A complete orbital phase coverage of WASP-33b with high-resolution spectroscopic (spectro-polarimetric) observations could help understanding the nature of the pre-transit signal.
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