In order to gain more information on the 236 M dwarfs identified in the First Byurakan Survey (FBS) low-resolution (lr) spectroscopic database, Gaia EDR3 high-accuracy astrometric and photometric data and Transiting Exoplanet Survey Satellite (TESS) data are used to characterise these M dwarfs and their possible multiplicity. Among the sample of 236 relatively bright $(7.3 < K_S < 14.4)$ M dwarfs, 176 are new discoveries. The Gaia EDR3 G broadband magnitudes are in the range $11.3 < G < 17.1$. New distance information based on the EDR3 parallaxes are used to estimate the G-band absolute magnitudes. Nine FBS M dwarfs out of 176 newly discovered lie within 25 pc of the Sun. The FBS 0909-082 is the most distant $(r=780$ pc) M dwarf of the analysed sample, with a G-band absolute magnitude $M(G) = 9.18$, $M = 0.59$ M$_{\odot}$, $L = 0.13597$ L$_{\odot}$, and $T_{eff}$ = 3844 K; it can be classified as M1 - M2 subtype dwarf. The nearest is FBS 0250+167, a M7 subtype dwarf located at 3.83 pc from the Sun with a very high proper motion (5.13 arcsec yr$^{-1}$). The TESS estimated masses lie in the range 0.095 ($\pm$0.02) M$_{\odot}\leq$ $M\leq$ 0.7 ($\pm$ 0.1) M$_{\odot}$ and $T_{eff}$ in the range 4000 K < $T_{eff}$ < 2790 K. We analyse colour-colour and colour-absolute magnitude diagram (CaMD) diagrams for the M dwarfs. Results suggest that 27 FBS M dwarfs are double or multiple systems. The observed spectral energy distribution (SED) for some of the M dwarfs can be used to classify potential infrared excess. Using TESS light curves, flares are detected for some FBS M dwarfs. Finally, for early and late sub-classes of the M dwarfs, the detection range for survey is estimated for the first time.