Here’s the evaluation of the sentences for correctness:

1. **Correct**
(He was a gifted songwriter, but he had to suffer poor health.)

2. **Incorrect**
("nor she likes its plot" should be "nor does she like its plot.")

3. **Correct**
(Pitt has just put two new batteries in the toy car, yet it is not running.)

4. **Correct**
(Mary was tired, yet we stopped for a rest.)

5. **Correct**
(It can be caused by human error, and maybe it is totally a coincidence.)

6. **Correct**
(You've been waiting for too long; you should go home, and I will ask Sally to talk to you later.)

7. **Correct**
(I stayed in San Francisco for two years, so that I can recommend some really nice sites.)

8. **Correct**
(Because my mother is busy this week, my father is going to my cousin's wedding.)

Let me know if you need any further help!