Original: When we had ate lunch, we were sitting in the garden.
Corrected: When we had eaten lunch, we sat in the garden.

Explanation: After the past perfect tense ("had"), we use the past participle form of the verb.
Original: While I looked for my keys, I remembered I left them at home.
Corrected: While I was looking for my keys, I remembered I had left them at home.

Explanation: We use the past continuous tense for the background action and the past perfect tense for the action that happened before.
Original: Paula had used to play tennis when she had been at school.
Corrected: Paula used to play tennis when she was at school.

Explanation: "Used to" is used to express past habits or repeated actions.
Original: When I got into bed, I was falling asleep immediately.
Corrected: When I got into bed, I fell asleep immediately.

Explanation: "Fell asleep" is a past simple tense, used to express a completed action.
Original: When I was finally finding the house, I was knocking at the door.
Corrected: When I finally found the house, I knocked at the door.

Explanation: Both actions happened one after the other in the past, so we use the past simple tense for both.
Original: After Jill was giving Nick his books, she went home.
Corrected: After Jill had given Nick his books, she went home.

Explanation: The action of giving the books happened before the action of going home, so we use the past perfect tense.
Original: Maria would live in Sweden when she was a child.
Corrected: Maria used to live in Sweden when she was a child.

Explanation: "Used to" is used to express past habits or repeated actions.
Original: I was using to get up early when I had gone sailing.
Corrected: I used to get up early when I went sailing.

Explanation: "Used to" is used to express past habits or repeated actions.
Original: The Vikings had sailed to North America a thousand years ago.
Corrected: The Vikings sailed to North America a thousand years ago.

Explanation: The action happened in the past, so we use the past simple tense.
Original: Juliet was sure she was seeing the tall man before.
Corrected: Juliet was sure she had seen the tall man before.

Explanation: The action of seeing the tall man happened before the main action (being sure), so we use the past perfect tense.