First measurement of Mg isotope abundances at high redshifts and accurate estimate of Delta alpha/alpha

(Abridged) We use a high-resolution spectrum of the quasar HE0001-2340 observed with the UVES/VLT to measure Mg isotope abundances in the intervening absorption-line systems at high redshifts. Line profiles are prepared accounting for possible shifts between the individual exposures. Due to unique composition of the selected systems - the presence of several transitions of the same ion - we can test the local accuracy of the wavelength scale calibration which is the main source of errors in the sub-pixel line position measurements. In the system at zabs = 0.45 which is probably a fragment of the outflow caused by SN Ia explosion of high-metallicity white dwarf(s) we measured velocity shifts of MgII and MgI lines relative to other lines (FeI, FeII, CaI, CaII): Delta V(MgII) = -0.44 +/- 0.05 km/s and Delta V(MgI) = -0.17 +/- 0.17$ km/s. This translates into the isotopic ratio 24Mg:25Mg:26Mg = (19 +/- 11):(22 +/- 13):(59 +/- 6) with a strong relative overabundance of heavy Mg isotopes, (25Mg+26Mg)/24Mg = 4, as compared to the solar ratio 24Mg:25Mg:26Mg = 79:10:11, and (25Mg+26Mg)/24Mg = 0.3. At zabs = 1.58, we put a strong constraint on a putative variation of alpha: Delta alpha/alpha = (-1.5 +/- 2.6)x10^{-6} which is one of the most stringent limits obtained from optical spectra of QSOs. We reveal that the wavelength calibration in the range above 7500 A is subject to systematic wavelength-dependent drifts.