How to estimate standard error of journal impact factor based on impact factor and number of citable papers?
I think the standard error (of the mean, commonly estimated as s/sqrt(n) as stated in the OP) is a robust and good estimate for the uncertainty of the impact factor. It would certainly be interesting to know this together with the impact factors. Unfortunately, the standard error cannot be computed merely from the impact factor and the number of citable papers.

Note that the impact factor, being the average citation count, follows a normal distribution, even if the citation counts themselves don't (according to the central limit theorem).

A completely different question is whether, in view of skewed distributions of citation counts, the traditional impact factor (=average citation count) is a good measure for journal impact.