The magnetic structure and the multiferroic relaxation dynamics of NaFeGe$_2$O$_6$ were studied by neutron scattering on single crystals partially utilizing polarization analysis. In addition to the previously reported transitions, the incommensurate spiral ordering of Fe$^{3+}$ moments in the $ac$ plane develops an additional component along the crystallographic $b$ direction below $Tapprox 5text{ K}$, which coincides with a lock-in of the incommensurate modulation. The quasistatic control of the spin-spiral handedness, respectively of the vector chirality, by external electric fields proves the invertibility of multiferroic domains down to the lowest temperature. Time-resolved measurements of the multiferroic domain inversion in NaFeGe$_2$O$_6$ reveal a simple temperature and electric-field dependence of the multiferroic relaxation that is well described by a combined Arrhenius-Merz relation, as it has been observed for TbMnO$_3$. The maximum speed of domain wall motion is comparable to the spin wave velocity.
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