We present JWST Near-Infrared Spectrograph (NIRSpec) observations in integral field spectroscopic (IFS) mode of the galaxy GS5001 at redshift z=3.47, the central member of a candidate protocluster in the GOODS-S field. The data cover a field of view (FoV) of $4 kpc$^2$) and were obtained as part of the Galaxy Assembly with NIRSpec IFS (GA-NIFS) GTO programme. The observations include both high (Rsim 2700) and low (Rsim 100) spectral resolution data, spanning the rest-frame wavelength ranges 3700-6780 and 1300-11850 respectively. These observations enable the detection and mapping of the main optical emission lines from to We analysed the spatially resolved ionised gas kinematics and interstellar medium properties, including obscuration, gas metallicity, excitation, ionisation parameter, and electron density. In addition to the main galaxy (GS5001), the NIRSpec FoV covers a close companion in the south, with three sub-structures with velocities blueshifted by $ with respect to GS5001, and another source in the north redshifted by $ Optical line ratio diagnostics indicate star formation ionisation and electron densities of $ $ across all sources in the FoV. The gas-phase metallicity in the main galaxy is 12+log(O/H) $= 8.45 and slightly lower in the companions (12+log(O/H)$ = 8.34-8.42$), consistent with the mass-metallicity relation at $z We find peculiar line ratios (high log $, low log $) in the northern part of GS5001. These could be attributed to either higher metallicity, or to shocks resulting from the interaction of the main galaxy with the northern source. We identify a spatially resolved outflow in the main galaxy, traced by a broad symmetric component in and with an extension of about 3 kpc. We find maximum outflow velocities of $ an outflow mass of $(1.7 a mass outflow rate of $23 and a mass loading factor of 0.23. These properties are compatible with star formation being the driver of the outflow. Our analysis of these JWST NIRSpec IFS data therefore provides valuable, unprecedented insights into the interplay between star formation, galactic outflows, and interactions in the core of a $z 3.5$ candidate protocluster.