Context. Massive stars are among the main cosmic engines driving the evolution of star-forming galaxies. Their powerful ionising radiation and stellar winds inject a large amount of energy in the interstellar medium. Furthermore, mass-loss (Ṁ) through radiatively driven winds plays a key role in the evolution of massive stars. Even so, the wind mass-loss prescriptions used in stellar evolution models, population synthesis, and stellar feedback models often disagree with mass-loss rates empirically measured from the UV spectra of low metallicity massive stars. Aims: The most massive young star cluster in the low metallicity Small Magellanic Cloud galaxy is NGC 346. This cluster contains more than half of all O stars discovered in this galaxy so far. A similar age, metallicity (Z), and extinction, the O stars in the NGC 346 cluster are uniquely suited for a comparative study of stellar winds in O stars of different subtypes. We aim to use a sample of O stars within NGC 346 to study stellar winds at low metallicity. Methods: We mapped the central 1’ of NGC 346 with the long-slit UV observations performed by the Space Telescope Imaging Spectrograph (STIS) on board of the Hubble Space Telescope and complemented these new datasets with archival observations. Multi-epoch observations allowed for the detection of wind variability. The UV dataset was supplemented by optical spectroscopy and photometry. The resulting spectra were analysed using a non-local thermal equilibrium model atmosphere code (PoWR) to determine wind parameters and ionising fluxes. Results: The effective mapping technique allowed us to obtain a mosaic of almost the full extent of the cluster and resolve stars in its core. Among hundreds of extracted stellar spectra, 21 belong to O stars. Nine of them are classified as O stars for the first time. We analyse, in detail, the UV spectra of 19 O stars (with a further two needing to be analysed in a later paper due to the complexity of the wind lines as a result of multiplicity). This more than triples the number of O stars in the core of NGC 346 with constrained wind properties. We show that the most commonly used theoretical mass-loss recipes for O stars over-predict mass-loss rates. We find that the empirical scaling between mass-loss rates (Ṁ) and luminosity (L), Ṁ ∝ L2.4, is steeper than theoretically expected by the most commonly used recipes. In agreement with the most recent theoretical predictions, we find within Ṁ ∝ Zα that α is dependent upon L. Only the most luminous stars dominate the ionisation feedback, while the weak stellar winds of O stars in NGC 346 and the lack of previous supernova explosions in this cluster restrict the kinetic energy input.