No statistical significance between group means determined by ANOVA After performing a one-way analysis of variance (ANOVA) and determining that there is no statistical significances between group means is it permissible to then aggregate the means to obtain a “grand” mean and confidence interval for the population. 
 A: Yes and no.
No because the results of a "fail to reject" finding means either there is no difference or you did not have enough power to detect a difference. We never conclude that the null is true as the result of a null finding. Plenty of evidence that we collect is consistent with incorrect hypotheses. That is why we state them first, then falsify them.
Yes because the data are meaningful insofar as they were collected as part of a study. You can summarize grand aspects of that sample and, using a confidence interval, infer what range of values this mean is consistent with. For instance, in public health data, you may collect evidence on BMI and race with the hypothesis that BMI differs in race groups. The grand average BMI and its 95% CI summarizes the variability in your data as well as the general trend. If the data are nationally representative, they summarize the current state of the nation. It contextualizes how "big" some differences are, in case some appear to be "clinically meaningful" (such as a difference of 5 kg/m^2) but not statistically significant.
Basically, it is all a matter of how you report it.
A: In a certain sense you could do this even if the means were different, the overall mean would be an estimate of the expected value of the marginal distribution, averaged over the various groups.
What is your goal in doing this?  That would probably give a better sense of whether or not it's appropriate.
A: I think you're asking the wrong question. My advice is to get out of star-gazing mode (i.e., focusing solely on asterisks) and look at the numbers you have. 
Write down the means for each group and ask a colleague (or yourself, for that matter) whether s/he thinks there are any practical or meaningful or important differences among them. If no, then it makes sense to pool them together and report the result. If yes, then you obviously don't have enough data to establish that those important differences are statistically detectable. 
(And BTW your post hoc power calculation can't help you judge whether you have enough data.)
A: Yes.
The way to construct a confidence interval must of course match de distribution of your population, but as you are putting multiple groups together, you should have enough observations to apply the central limit theorem.
A: I would suggest visualizing the distributions with histograms and boxplots. If they look similar and there is a meaningful reason to combine them, like having a better estimate of the mean and a tighter confidence interval, then it may be fine. It would be inappropriate however to report this mean as a conclusion that there are definitively no group differences. Also make sure you have not violated any ANOVA assumptions. For example, if there is drastically different variation in the group distributions you should look into a non parametric 1-way ANOVA.
