In the US (in Texas where I grew up anyway) I would be more likely to say "it is true" if the context was "Do she really do that? Yes, it is true" I might also use "Yes, it is so" to mean it truly happened. Sometimes someone would say "it is so", with increasing emphasis on the latter part of the sentence as a rebuttal to something like "That cannot be true" I have never heard the phrase used in any other way, i.e., so = true.
'Like so', or 'like this', or 'this is the way" , and even "this is how" is correct. We don't really know the context. They are all acceptable in a situation when someone shows how to do something. There is another possibility: a reference to how the world (life) is: this is how things are. Maybe that's what they mean. And yes, it can be a set expression of idiomatic nature except they don't explain it, or any of our theories. On top of it, what they shouldn't do is to stop us from doing the next exercise. After all, this is not about English, especially when there are no explanations but just guesses on the part of students. This is all about Italian.