What techniques can be used to differentiate between correlation and causation?
There is no statistical test for distinguishing mere correlation from causation. It has to come from ulterior (model) considerations.
Having said that, a common way is to design a new experiment, called a controlled study, in which [based on ulterior model considerations] you change something in some but not all the items/subjects observed. This is basically what you describe (propose to do) in your situation 1.
If you have no way whatsoever to change/adjust anything, then you are stuck so to speak; there's no way to go beyond observational studies. In practice, researchers come up with an idea of what causes what and try to &quot;eliminate&quot; (or rather account for) confounders--what you call an &quot;external factor&quot;. There are various degrees of statistical sophistication at which you can do this, e.g. the so called path analysis. However, coming up with a complete list of confounders is hopeless.

A science in which by necessity many or most studies are observational is called an observational science (duh). Psychology is not the only science where you find a lot of observational studies. Archeology, geology, epidemiology or astronomy are other, perhaps more exterme examples. In general, a science being (mostly) observational entails that it's more difficult to replicate the results of studies findings... but some contend that this state of affairs is something people got used to... so the so-called &quot;replication crisis&quot; has mostly to do with controlled rather than observational studies. Quoting from the previous link:


But Peng also describes his own field, epidemiology, in the top left of the chart, as having largely been spared the reproducibility crisis, even though it is as theoretically rudderless as medicine or psychology (or archaeology). His contention is that in fields that rely on experimentation, breeds an unreasonable expectation that the results of single experiments (if well-designed and statistically validated) are true. Meanwhile, observational sciences, which are accustomed to the fact that they have little control over their observations and that single results may well be wrong, have already learned the core lesson of the reproducibility crisis: don’t trust that that isn’t replicated.

In fact some of the most controversial results in psychology have both a theoretical (albeit not deeply so) basis and rely on controlled rather that observational studies, e.g. the ego depletion hypothesis, which is roughly that sugar restores willpower.