Spectroscopically, TDEs are characterized by broad ( 10$^{4}$ km/s) emission lines and show large diversity as well as different line profiles. After carefully and consistently performing a series of data reduction tasks including host galaxy light subtraction, we present here the first detailed, spectroscopic population study of 16 optical/UV TDEs. We report a time lag between the peaks of the optical light-curves and the peak luminosity of H$alpha$ spanning between 7 - 45 days. If interpreted as light-echoes, these lags correspond to distances of 2 - 12 x 10$^{16}$ cm, one to two orders of magnitudes larger than the estimated blackbody radii (R$_{rm BB}$) of the same TDEs and we discuss the possible origin of this surprisingly large discrepancy. We also report time lags for the peak luminosity of He I $lambda$5876 line; smaller than the ones of H$alpha$ for H TDEs and similar or larger for N III Bowen TDEs. We report that N III Bowen TDEs have lower H$alpha$ velocity widths compared to the rest of the TDEs in our sample and we also find that a strong X-ray to optical ratio might imply weakening of the line widths. Furthermore, we study the evolution of line luminosities and ratios with respect to their radii (R$_{rm BB}$) and temperatures (T$_{rm BB}$). We find a linear relationship between H$alpha$ luminosity and the R$_{rm BB}$ and potentially an inverse power-law relation with T$_{rm BB}$ leading to weaker H$alpha$ emission for T$_{rm BB}$ $geq$ 25000 K. The He II/He I ratio becomes large at the same temperatures possibly pointing to an ionization effect. The He II/H$alpha$ ratio becomes larger as the photospheric radius recedes, implying a stratified photosphere where Helium lies deeper than Hydrogen. We suggest that the large diversity of the spectroscopic features seen in TDEs along with their X-ray properties, can potentially be attributed to viewing angle effects.
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