  We present pure spectroscopic constraints on the UV luminosity functions and
cosmic star formation rate (SFR) densities from 25 galaxies at
$z_\mathrm{spec}=8.61-13.20$. By reducing the JWST/NIRSpec spectra taken in
multiple programs of ERO, ERS, GO, and DDT with our analysis technique, we
independently confirm 16 galaxies at $z_\mathrm{spec}=8.61-11.40$ including new
redshift determinations, and a bright interloper at $z_\mathrm{spec}=4.91$ that
was claimed as a photometric candidate at z~16. In conjunction with nine
galaxies at redshifts up to $z_\mathrm{spec}=13.20$ in the literature, we make
a sample of 25 spectroscopically-confirmed galaxies in total and carefully
derive the best estimates and lower limits of the UV luminosity functions.
These UV luminosity function constraints are consistent with the previous
photometric estimates within the uncertainties and indicate mild redshift
evolution towards z~12 showing tensions with some theoretical models of rapid
evolution. With these spectroscopic constraints, we obtain firm lower limits of
the cosmic SFR densities and spectroscopically confirm a high SFR density at
z~12 beyond the constant star-formation efficiency models, which supports
earlier claims from the photometric studies. While there are no
spectroscopically-confirmed galaxies with very large stellar masses violating
the $\Lambda$CDM model due to the removal of the bright interloper, we confirm
star-forming galaxies at $z_\mathrm{spec}=11-13$ with stellar masses much
higher than model predictions. Our results indicate possibilities of high
star-formation efficiency (>5%), hidden AGN, top-heavy initial mass function
(possibly with Pop-III), and large scatter/variance. Having these successful
and unsuccessful spectroscopy results, we suggest observational strategies for
efficiently removing low redshift interlopers for future JWST programs.
