Questions Aabout English Tenses

1. In the afternoons he was playinged darts or reading a book / In the afternoon's he would played darts or read a book.

past tense / past something ...

(Are both of these versions correct? What's the difference in meaning between them? )

In my corrections, there's not much of a difference. They're both past tense.

(Are both versions possible? )

Yes, good work.

(Are they correct? How does the meaning change? )

Yes, these are both correct but we say the second way much more often in the US. There's no change in meaning between the two.

(Is the first option an assumption that she didn’t pass thate exam and the second option is just general information about the consequences of her not passing the exam? )

No, both mean the same thing.

(Is the first option "I didn’t see her for 3 months"at all correct? Does the second one mean "She's been out of my sight for 3 months, however, I could have been maessaging her online"? Does the third one mean that the person has not been dating some womanone for 3 months? )

1 is correct.
2 is correct and more commonly used in the US. 1 and 2 mean the same thing. This usually means you've had no contact with the person.
3 You're correct in that it means that they haven't been dating for 3 months.

6. He has been playing chess for years but has not made much progress - h. He still plays / he's still playing chess but he still isn't good.

(Which of the two options is more natural to use to explain the part of the sentence before athe dash, which referrings to him as still playing chess and still not being good? )

1 and 2 mean the same thing and both are correct as well as natural.

7. In relationgards to the previous question, does "HE PLAYED CHESS FOR SOME YEARS AND HE STILL PLAYS CHESS" have the same meaning as "HE HAS BEEN PLAYING CHESS FOR YEARS?"

1 doesn't sound natural to me. 2 is much more natural to me.

1. In the afternoons he was playing darts or reading a book / In the afternoon's he played darts or read a book.

(Are both these versions correct? What's the difference in meaning between them? )

These are both correct grammatically, although I changed your spelling. And yes, these are basically the same, to the point where they can be used interchangeably.

(Are both versions possible? )

Yes, both versions are possible.

(Are they correct? How does the meaning change? )

The meaning does not change, they can be used interchangeably.

(Is the first option an assumption that she didn’t pass that exam and the second option is just general information about the consequences of her not passing the exam? )

The first sentence says that she has already taken her exam and the speaker does not know the results. The second sentence is general information about consequences. The first does not make any assumptions besides assuming that she has already taken the exam.

(Is the first option "I didn’t see her for 3 months"at all correct? Does the second one mean "She's been out of my sight for 3 months, however I could have been massaging her online"? Does the third one mean that the person has not been dating some woman for 3 months? )

The first and second options mean the same thing, that the speaker hasn't been in contact with the woman for three months. Their only difference is that the first means that the speaker has recently seen her, but before that they did not see her for three months. The second means that they have not been in contact with the woman at all, and it has recently been three months since last contact. The third one usually means the woman and the speaker haven't been dating for three months, but in the southern United States, it has the same meaning as the second.

(Which of the two options is more natural to use to explain the part of the sentence before a dash, referring to him as still playing chess and still not being good? )

"He still plays" is more natural, as "he's still playing" implies he is currently playing a game of chess, and not that he regularly plays chess.

7. In relation to the previous question, does "HE PLAYED CHESS FOR SOME YEARS AND HE STILL PLAYS CHESS" have the same meaning as "HE HAS BEEN PLAYING CHESS FOR YEARS?"

Yes, both have the same meaning. However, the first sentence is redundant, as the second sentence provides the same amount of information.