The phrase 'valuable insights' is correct and can be used in written English. You can use it to refer to ideas, opinions, or wisdom that is worth taking into account or given special consideration. For example, "This research on market trends provides valuable insights for our business decisions.".

You can use it when referring to someone (or something) providing information that leads to a deeper understanding of the topic. For example: "The expert's analysis offered valuable insights on the current state of the economy."

"gain valuable insights" is a correct phrase in written English. It is generally used as a way to talk about gaining a better understanding of something through research or experience. For example, "Through her internship, she was able to gain valuable insights into the world of business."