I have the following "Reorted Speech" sentences and I would like to ask a native speaker's opinion about them. Thank You.

1. When I am tired I always sleep a bit." he said. -> He said that he always sleeps?/slept? a bit when he is?/was? tired.

2. He said that his wife is?/was? a wonderful mother.

3. Did you hear? She said she was?/is? forty years old.

4.He said the eart goes/went round the sun. ->

5. "I will help you tomorrow" he said. -> A, He said that he will help me tomorrow. (correct?)
B, He said that he would help me the next day. (and what about tis one?)

6. "I was learning when my parents arrived" said the little boy.
A, The little boy said that he was just learning when his parents arrived.
B, The little boy said that he had just been learning when his parents arrived.

7. "When I was living in Gyor I often saw Peter" said Annie to me. ->
A, Annie told me that she often saw Peter when she was living in Gyor.
B, Annie told me that she often had seen Peter when she had been living in Gyor. (which one is good? Why?)
I am not a native English speaker, but I'll have my shot at this.

1. "When I am tired I always sleep a bit," he said.
- You use the simple present tense of sleep because he does it habitually.
2. It depends. Is his wife still a mother (children still alive)? Did he say this referring how his wife was a good mother (children are grown-up and no longer dependent on their parents)?
3. She said she is forty years old. This is assuming that this whole conversation happened just now. If this was a dialogue you are referring to happened years back, then the woman might no longer be 40 years old, so in this case, you would use was.
4. He said that the Earth goes around the sun. It is a habitual, a general, or an always true statement (except when Venus gets engulfed by the sun's heat with Earth after it).
A. Yes, that's correct.
B. Yes, that's correct, too.
6. This is vague--learning what?
A. One way to put it.
B. No.
- This sentence is what is called past progressive tense. It is when a past action is happening when another action occurs.
A. Correct.
B. I don't think "had seen" is standard. You could use "had been seeing" instead. Don't quote me on that because I ain't sure.
The first intepretation is the correct interpretation. Be careful not to restructure sentence A to "while she was living in Gyor, Annie told me that she often saw Peter." I just though I should mention that.
Jacko: couple of things I'd change.

6B - It was ok, his original explaination was vague, but I see what he meant.
7B - "had seen" can be used (not quite as he/she used it though), "I had seen him walking..", "If I had seen it sooner", "she had often seen.."
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a number of these sentences are correct, but much of it depends on whether the actions fall completely or partially in the past/present/future. look up "indirect discourse" in whatever grammar you are using and "concordance of verb tenses" which might give you some specific examples. i can't give you much more help without contextualizing the sample sentences you have provided.
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One thing that I could add to the discussion is that when writing the reported speech, the general rule is that you move one step in the past in the reported speech.

go changes to went and went to had gone:

go ---- went

went ---- had gone


Direct Speech: "He goes to school everyday," she said.

Reported speech: She said that he went to school everyday.

Add to this the fact that if the action (here going to school) is still true in the present, the reported speech could be in the present as well. Thus, we can say the following:

Reproted Speech: She said that he goes to school everday. (going to school is still true today).

Summary of the Reported Speech:

Always change the verbs one step in the past. It is O.K. if you use the present tense or the future tense (will or be going to) when the action can be true of the present or future.

"He is going to go to school tomorrow," she said.

She said he was going to school tomorrow.

She said he is giong to go to school tomorrow.

I hope I have added some to the discussion of reported speech.