Yes! Native speakers DO use indirect speech in everyday situations when speaking, and the rules come perfectly naturally to us. You just step back one stage into the past : present tense becomes a past tense, and past tense becomes past perfect. It's simple, logical and instinctive - there's nothing weird or crazy at all. We don't even think about it. The so-called teacher you heard saying this - "Indirect speech is usually only used for writing, so we don't really have to worry about all of these crazy rules when we speak". - was talking utter nonsense. Why did he or she say this? The only reason I can think of is that this person wanted to sound cool, friendly and fun, and earn lots of likes by saying what students wanted to hear. Unfortunately, it is completely untrue. Moorad, I think that the most important lesson you can learn from this post is to ignore YouTube 'teachers'. In the past, students learnt from reliable textbooks and from experienced qualified teachers, and you could trust them. These days, unfortunately, any unqualified or ignorant person can call themselves an expert, make a video and put themselves on the internet. Don't trust everything you see on Youtube!

Yes we do, and we do it often. The benefit of reported speech is that we have extra freedom to paraphrase if we wish. I'd say we prefer reported speech more than quoting people directly. What is causing you confusion?

Yes, we do. They don't seem weird to us! Hopefully, a good grammar book should indicate if a rule is not normally followed, or perhaps is only for formal speech.

She said, "I saw him." (direct speech) = She said that she had seen him. (indirect speech) Direct speech: “I like ice cream”. Reported speech: She says (that) she likes ice cream. Direct speech: “The sky is blue”. Reported speech: She said (that) the sky is/was blue. I would say that Reported or Indirect speech is mainly used in the news etc... but of course nothing prevents you from using it for a reporting statements or reporting questions.

What's examples are you thinking about ?