Context. Malin 1 is the largest known low surface brightness (LSB) galaxy, the archetype of so-called giant LSB galaxies. The structure and origin of such galaxies are still poorly understood, especially because of the lack of high-resolution kinematics and spectroscopic data. Aims. We use emission lines from spectroscopic observations of Malin 1 aiming to bring new constraints on the internal dynamics and star formation history of Malin 1. Methods. We extracted a total of 16 spectra from different regions of Malin 1 and calculated the rotational velocities of these regions from the wavelength shifts and star formation rates from the observed Hα emission line fluxes. We compared our data with existing data and models for Malin 1. Results. For the first time we present the inner rotation curve of Malin 1, characterised in the radial range r < 10 kpc by a steep rise in the rotational velocity up to at least ∼350 km s−1 (with a large dispersion), which had not been observed previously. We used these data to study a suite of new mass models for Malin 1. We show that in the inner regions dynamics may be dominated by the stars (although none of our models can explain the highest velocities measured) but that at large radii a massive dark matter halo remains necessary. The Hα fluxes derived star formation rates are consistent with an early-type disc for the inner region and with the level found in extended UV galaxies for the outer parts of the giant disc of Malin 1. We also find signs of high metallicity but low dust content for the inner regions.