In the first sentence, the person had different, countable experiences, each of which gave her a distinct insight e.g. into the food, the family traditions. In the second sentence, the sense is more "I hope you now understand more deeply ..." This kind of knowledge is more general in nature. We are not talking of it as a collection of things which can be counted. You could make the first sentence uncountable and the second countable, if you considered the insight(s) in the ways I mentioned. It depends on your meaning. There is another, psychological meaning of "insight" which is uncountable. This insight is the capacity to understand the significance of one's actions. It is close in meaning to "awareness".

The difference between "some insight" and "insights" is subtle. In the first sentence, Mexican life is assumed to be complex. It is assumed that there are many moments (while reading) in which the reader will say, "AH! I understand!". Each of those moments is //an insight// (event: a moment of understanding). Each moment gives us //some insight// (some knowledge, uncountable) into Mexican life. Do you see the difference here? The book is giving us discrete //moments//. Each moment is //an insight// into Mexican life. Therefore the book is giving us many insights -- plural insights. Each moment adds to our general knowledge of, our (uncountable) insight into, Mexican life. ------------- Consider the second sentence: "I hope you have gained some insight into the difficulties we face." It is not describing any kind of "moment", instead it is like saying, "I hope you gained some knowledge". You could rewrite it to use a countable insight as following: "I hope this meeting has given you an insight into the difficulties we face" (singular event -> singular insight) "I hope these meetings have given you many insights into the difficulties we face." (plural meetings -> plural insights)

The book gives us fascinating insights into life in Mexico. The plural is used here because it is probably assumed that the reader of the book has learned more than one thing about life in Mexico. I hope you gained some insight into the difficulties we face. The singular is used here because it is hoped that the person has gained at least one bit of knowledge. Either form could be used in both sentences depending on the context, assumptions, hopes, etc...