What does it mean for a sample size to be "too low", in terms of estimation vs inferrence? We often hear of studies with "too low" a sample size. But what does that actually mean? Is it perhaps any of these two things (if not, please suggest a better interpretation):
1) Inability to reject a certain null hypothesis, given a certain expected effect size and power level.
2) Too poor an estimate of the population mean given the sample mean. (see follow-up questions on this below)
2.1) How is a "good enough" such estimate defined?!
2.2) Does the computation of such an estimate qualify as inference or as interval estimation, and is it not true that computing confidence intervals achieves both aims? I ask because I know that advocates of statistical reform suggest emphasis should swing from NHST to statistical estimation, but I don't see how one could do one without the other 
I apologise for this question mixing up several different questions, but I found no way to ask in a way that disambiguates the different issues.
 A: Saying that the sample is too small is not a formal statement; it's merely a judgment of dissatisfaction with the sample size. Specific reasons to be dissatisfied, depending on the analysis and the data, include low anticipated power, wide confidence intervals, and large anticipated error in point estimates.

Does the computation of such an estimate qualify as inference or as interval estimation

Interval estimation is a kind of estimation, which is a kind of inference. You're doing interval estimation when you estimate a quantity with an interval that's supposed to contain the true value (such as a confidence interval or credible interval), and point estimation if you estimate the quantity with a point (i.e., a single value).

[regarding NHST vs. estimation] I don't see how one could do one without the other

If you compute a sample mean and declare it to be an estimate of the population mean, you've estimated something without performing a significance test. Whether the converse is possible (doing a significance test without estimating anything) is kind of a matter of semantics (if the only thing you do with a sample correlation coefficient is check whether it's significantly different from 0, does that count as estimating the population correlation coefficient?).
