Giant low surface brightness galaxies (gLSBGs) with dynamically cold stellar discs reaching the radius of 130 kpc challenge currently considered galaxy formation mechanisms. We analyse new deep long-slit optical spectroscopic observations, archival optical images and published H and optical spectroscopic data for a sample of seven gLSBGs, for which we performed mass modeling and estimated the parameters of dark matter haloes assuming the Burkert dark matter density profile. Our sample is not homogeneous by morphology, parameters of stellar populations and total mass, however, six of seven galaxies sit on the high-mass extension of the baryonic Tully-Fisher relation. In UGC 1382 we detected a global counter-rotation of the stellar high surface brightness (HSB) disc with respect to the extended LSB disc. In UGC 1922 with signatures of a possible merger, the gas counter-rotation is seen in the inner disc. Six galaxies host active galactic nuclei, three of which have the estimated black hole masses substantially below those expected for their (pseudo-)bulge properties suggesting poor merger histories. Overall, the morphology, internal dynamics, and low star formation efficiency in the outer discs indicate that the three formation scenarios shape gLSBGs: (i) a two-stage formation when an HSB galaxy is formed first and then grows an LSB disc by accreting gas from an external supply; (ii) an unusual shallow and extended dark matter halo; (iii) a major merger with fine-tuned orbital parameters and morphologies of the merging galaxies.