1. When we had ate lunch, we were sitting in the garden.

• Error: "Had ate" is incorrect grammar.
• Correction: "When we had eaten lunch, we were sitting in the garden." (Past participle of "eat" is "eaten")

2. While I looked for my keys, I remembered I left them at home.

• Error: No error in the core sentence structure.
• Correction: The sentence is grammatically correct.

3. Paula had used to play tennis when she had been at school.

• Error: "Had used to" is redundant. "Used to" already expresses past habit.
• Correction: "Paula used to play tennis when she was at school." (Simplify and use past simple tense)

4. When I got into bed, I was falling asleep immediately.

• Error: No major error, but "was falling" sounds awkward.
• Correction: You can keep it the same or rephrase as "When I got into bed, I fell asleep immediately." (Simple past for a completed action)

5. When I was finally finding the house, I was knocking at the door.

• Error: "Was finding" suggests a continuous search while arriving.
• Correction: "When I finally found the house, I was knocking at the door." (Simple past for a completed action of finding)

6. After Jill was giving Nick his books, she went home.

• Error: "Was giving" suggests an action in progress.
• Correction: "After Jill gave Nick his books, she went home." (Simple past for a completed action)

7. Maria would live in Sweden when she was a child.

• Error: "Would live" suggests a future action in the past, which is nonsensical.
• Correction: "Maria lived in Sweden when she was a child." (Simple past for a completed action in the past)

8. I was using to get up early when I had gone sailing.

• Error: Similar to sentence 3, "was using to" is redundant.
• Correction: "I used to get up early when I went sailing." (Simplify and use past simple tense)

9. The Vikings had sailed to North America a thousand years ago.

• Error: No error, the sentence is grammatically correct.

10. Juliet was sure she was seeing the tall man before.

• Error: No major error, but "was seeing" is a bit awkward.
• Correction: You can keep it the same or rephrase as "Juliet was sure she had seen the tall man before." (Past perfect for an action completed before another past action)