Highly turbulent nature of convection on the Sun causes strong multi-scale interaction of subsurface layers with the photosphere and chromosphere. According to realistic 3D radiative MHD numerical simulations ubiquitous small-scale vortex tubes are generated by turbulent flows below the visible surface and concentrated in the intergranular lanes. The vortex tubes can capture and amplify magnetic field, penetrate into chromospheric layers and initiate quasi-periodic flow eruptions that generates Alfvenic waves, transport mass and energy into the solar atmosphere. The simulations revealed high-speed flow patterns, and complicated thermodynamic and magnetic structures in the erupting vortex tubes. The spontaneous eruptions are initiated and driven by strong pressure gradients in the near-surface layers, and accelerated by the Lorentz force in the low chromosphere. In this paper, the simulation data are used to further investigate the dynamics of the eruptions, their spectro-polarimetric characteristics for the Fe I 6301.5 and 6302.5 A spectral lines, and demonstrate expected signatures of the eruptions in the Hinode SP data. We found that the complex dynamical structure of vortex tubes (downflows in the vortex core and upflows on periphery) can be captured by the Stokes I profiles. During an eruption, the ratio of down and upflows can suddenly change, and this effect can be observed in the Stokes V profile. Also, during the eruption the linear polarization signal increases, and this also can be detected with Hinode SP.