Need a native speaker's opinion

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).
5.
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.
7.
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.

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.