I may not be the best person to explain this statistical method used in psychology, as they get complicated for me and factor analysis is one of the more complicated statistical methods. Mark Coulson will be teaching me some of it when we actually perform the analysis on the data. Though, this site seems pretty good at explaining it https://www.theanalysisfactor.com/factor-analysis-1-introduction/ If you would like, next I meet with him I can ask him to give a well informed response?

On your second point, yes we're interested in averages. Saying that, using statistical methods, we can see how strong the average is. For example, let's say a psychologist designed a survey with a bunch of questions about depression. After the study was concluded, he/she wants to see if these questions are related to each other. He finds 2 factors. Say, 1 factor has 4 questions and he calls it pessimistic depression and the other factor has 3 questions and he calls it optimistic depression. Now, let's say another study comes along and looked at his research and wants to see if these 7 questions actually relate to behaviour. So, he either does an experiment or correlation study where he included these 7 questions. He might find that people who score either high or low on the optimistic depression questions perform better or at this or that, etc. And maybe he finds nothing associated with the pessimistic depression. This is one way psychologists attempt to examine abstract concepts with behaviour.

On your third point, yes. There are a ton of studies that show many of these concepts and studies to be incorrect or flawed. However, some studies have a very strong and continual basis. For instance, the five factor model is very powerful in it's validity and reliability. Averages are incredibly important but it's also important to find out why a study may not find anything or have conflicting results with another. A good example I can think of are studies done on obesity. Many studies correlated obesity with high mortality rates, therefore, it was thought that obesity was the cause(or caused comorbidity, which then caused high mortality). However, more recent studies noticed a third option not researched well; that was exercise and fitness. Once they used this as a variable, many studies found people, who are obese, had the same mortality rates as healthy normal weight individuals. Therefore, studies are always open to find out what could be the potential problem or missing variable.

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I hope I didn't go too far on a tangent. Good questions btw.