Stellar chemical abundances and kinematics provide key information for recovering the assembly history of galaxies. In this work we explore the chemo-chrono-kinematics of accreted and in situ stellar populations, by analyzing six M31/Milky Way (MW) analogues from the HESTIA suite of cosmological hydrodynamics zoom-in simulations of the Local Group. We show that elemental abundances ([Fe/H], [Mg/Fe]) of merger debris in the stellar haloes are chemically distinct from the survived dwarf galaxies, in that they are [α/Fe]-enhanced and have lower metallicity in the same stellar mass range. Therefore, mergers debris have abundances expected for stars originating from dwarfs that had their star formation activity quenched at early times. Accreted stellar haloes, including individual debris, reveal [Fe/H] and [Mg/Fe] gradients in the E − Lz plane, with the most metal-rich, [α/Fe]-poor stars, which have formed in the inner parts of the disrupted systems before the merger, contributing mainly to the central regions of the host galaxies. This results in negative metallicity gradients in the accreted components of stellar haloes at z = 0, seen also for the individual merger debris. We suggest, therefore, that abundance measurements of halo stars in the inner MW will allow constraining better the parameters, such as the mass and merger time, of MW's most massive merger Gaia-Sausage-Enceladus. The metallicity distribution functions (MDFs) of the individual debris show several peaks and the majority of debris have lower metallicity than the in situ stars in the prograde part of the E − Lz space. At the same time, non-rotating and retrograde accreted populations are very similar to the in situ stars in terms of [Fe/H] abundance. Prograde accreted stars show a prominent knee in the [Fe/H]-[Mg/Fe] plane, reaching up to solar [Mg/Fe], while retrograde stars typically contribute to the high-[Mg/Fe] sequence only. We find that the most metal-poor stars ([Fe/H] ≲ −1) of the HESTIA galaxies exhibit net rotation up to 80 km s−1, which is consistent with the Aurora population recently identified in the MW. At higher metallicities ([Fe/H] ≈ −0.5 ± 0.1) we detect a sharp transition (spin-up) from the turbulent phase to a regular disk-like rotation. Different merger debris appear similar in the [Fe/H]-[Mg/Fe] plane, thus making it difficult to identify individual events. However, combining a set of abundances, and especially stellar age, makes it possible to distinguish between different debris.