"Time reference changes when we use reported speech. For example: Anne said, ‘I’m going swimming this afternoon.’ ➟ Anne told me that she was going swimming that afternoon." Let's suppose that 'Anne' told me she was going swimming at 8 a.m., and that I reported what she had said to someone else at 11 a.m. of the same day; would it make sense to say "she was going swimming THAT afternoon". I believe the listener would assume that 'Anne' has already went swimming, and that I am talking about a previous day, rather than the one we are in. Am I right or wrong? Thanks in advance.
There are several examples and questions in your original post, so I'll try to break them down.
Let us first assume this is all today. It is now 11am. I spoke with Anne at 8am. At 8am, Anne said, "I am going swimming this afternoon."
Now, at 11am, I can say, "I spoke to Anne this morning. She said she was going swimming this afternoon."
If I said, "She said she was going swimming that afternoon", then there is some important context missing. We would first have to establish earlier in the conversation when "that" afternoon was.
So it might happen as follows:
A: Ann didn't come to lunch on Monday. Do you know why?
B: I spoke to Anne on Monday morning, actually. She said she was going swimming that afternoon.
This would make sense.