Likely Model
old solar population. single old burst or decreasing exponential SFR
subsolar (log(Z/Zsun)=-0.4 10 Gyr old burst, slightly younger than spectrum 1
large velocity dispersion, not sure the convolution has been done properly in the mock data. Looks like its constant FWHM in angstrom, not log(angstrom) Hence model lines are 1) too shallow in the blue  2) too deep in the red. Because of this its hard to get a really low chi^2. The residuals are similar in amplitude to what we would have with a S/N=300.
Since I cant get really low in chi^2 my interpretation is rather limited. My guess is a rather extended SFH , with a tentative second burst around 3 Gyr ago, just for the fun. The pop seems to be around solar metallicity.
Real spectrum: needed to mask 3720.,3740.],[4855.,4870.],[5000.,5020.],[6290.,6320.],[6540.,6600.],[6710.,6750.] Rather extended SFH. I dont really believe in the peaks of the best solution. I would need to regularize that better. Since the young young burst weighs only 1% in light, I dont really believe in it.
sorry, didn't do that one...
composite relatively old stuff: exponentially decreasing solar pop, about 10Gyr Luminosity-weighted age, with a supersolar burst around 3 Gyr
Same problem as spetrum no 3, unphysical convolution.  All I can see is an old solar pop. Possibly exponentially decreasing SFR

Technique used: STECKMAP, with a collection of SSP models.

left: Age-metallicity relation
middle: Stellar age distribution, i.e. the contribution to the total light vs age, i.e. these are flux fractions.
right: SFR. Note that this a SFR vs age, NOT MASSES! i.e. it can be
obtained as flux fractions (t) * (M/L(t) / extent of time bin).

Red line is the best fit.

Black thick line is the median of a number (between 10 and 5) MC sims,
in order to get error bars (thin vertical lines).

Generally if I know well the observational errors I would trust the
median of MC rather than the best fit.

Even though you apparently did not put flux calibration errors in your mock data, my code corrects for that, and I left this feature on. There are 30 nodes in the flux correction function.

Also the non-parametric kinematic deconvolution is on, and produces a nice gaussian in all cases even in 3 and 7.