To use text-processing functions, you must select some text first. If no text selected, TEA treats the whole text in a document as a selection. There are some special cases when TEA can treat the current word as selection when no text is actually selected. For example, it is a behavior of UPCASE and lowcase functions. But such behavior is a rare exception from the rule.
Document stats - outputs text statistics for the whole text or the selection into the Logmemo.
Document readability. Currently TEA implements two readability formulas: Automated Readability Index (ARI) and Coleman-Liau Index. I know that "its output approximates the U.S. grade level thought necessary to comprehend the text." (quote from Wikipedia), but I don't know how they are applicable to other languages than English.
You can notice that both result may vary from the results of Online readability tests. That's because of the difference in algorithms of sentences cound and word count calculations. TEA uses the standart GTK stuff for that and I think that is a right stuff.