It is not clear what you are trying to show a relationship between or predict however a couple of quick observations:

1. finding the 'best of the best' in relation to a number of possible predictors is often done using regression. This will indicate the contribution your predictors make to the outcome and the overall variance explained

2. if you are using correlation then the coefficient (eg r) will give you your effect size and there are standard tables for interpreting this

I hope this helps.

You might think of this type of research as confirmatory. You ran an experiment with workers in the field of inorganic chemistry. You got "this" answer. The next question is whether "this" answer is unique to scientists studying inorganic chemistry, or is it generally applicable to everyone in the sciences from archeology to zoology? Confirming the generality of your observations.

"best of the best" is risky even if all the independent variables (IV) are uncorrelated. You need to assume that none of the IV are correlated with any unmeasured variable(s). I assume that "best" will be determined by something like the smallest p-value, or highest r2. These numbers have confidence intervals. If you go back to collect more data, it is unlikely that the new data will exactly match the original data even if everything is the same as before. At best you hope that you arrive at the same conclusions as before. A confidence interval will help you make that assessment.

I don't think this question makes sense. Suppose you use a variable selection method such as lasso or gradient boosting. Here you would get the best result you can given the algorithm and the data set. If you change the algorithm, some algorithms give different results because they are unstable. If you change the experiment then you don't expect the same results necessarily. If the experiments are the same and the lab is changed you expect the results to be the same, i.e. the experiment is capable of being reproduced a fundamental idea of science. Thus I don't see how your suggestion can work. See the paper below for an example, Best, David Booth