Solver & Population size, any data analysts mathematicians that can point me?

Each regression analysis should go through the standard 7 assumptions. If all 5 of the 7 assumptions are met, it is a best linear unbiased estimator. If all 7 assumptions are met, it is a best unbiased estimator. See Gauss-Markov theorem, et al.

It really depends on the analyst and how much "feel" they have for the data. If you have gone through your data, model, and analysis and feel that you have explored all the problems and solutions possible then your analysis is sound. However, for me, analysis never ends and each question leads to further analysis.

Are you able to do a scatter plot and/or histogram of your data? Any noticeable frequency/distribution/cluster?