Are there any documented cases of meta-science or scientific meta-research? Does that have a name? Research is an activity, a process to obtain knowledge, which has been greatly empowered by the scientific method. 

We can collect lots of information about research, consider impact factors, etc.

There is data and information there, that data could possibly become knowledge through some analysis, hypothesis testing, and in general terms research. So what I'm talking about here is research about research, meta-research.

First of all, I'm interested to know whether this has been done in the past.

Second, if this has been done (I guess so), I would like to know by what name, so that I can search for it. It's easier to find information about fluid dynamics when you know it stands by the name of fluid dynamics.

BTW: I'm not interested in philosophy or epistemology, but science and hard verifiable facts.

There may be some lack of that, whatever that is. Related article: Scientific method: Statistical errors
Philosophy of Science, History of Science, Sociology of Science, Scientometrics to name a few meta-sciences.

(General trick for meta-science: use X of Science, where X is a science.
To generalize it even further, for meta-X, use X of Y, for some X in Y.)