Here are the suggested completions for each of the sentences:

2. In spite of his headache, he did well in the exam.
Although **he was in pain**.

3. They came to the concert late, so they didn't have good seats.
Had **they arrived earlier**.

4. Do your homework first, and I'll let you play the computer games.
I won't allow **you to play until then**.

5. It was a long time ago when I saw a movie.
It is **still fresh in my memory**.

6. My younger brother finally managed to get a job.
My younger brother was **very excited**.

7. They have just sold the old house at the end of the road.
The old house **has been vacant**.

8. You needn't finish the work today.
There's **no rush**.

Feel free to adjust any of the suggestions as needed!