The lLast week. Last week

Since it's a title, you don't need to have the full sentence.

The lLast week. Last week.

The lLast week l went to my cousin's house. Last week l went to my cousin's house.

You don't need a 'the' here.

The lLast week, l went to my cousin's house Last week, l went to my cousin's house

The native text implies that this is actually supposed to be plural, not singular. To attach a possessive to a plural word ending in "s", we just put the apostrophe at the end. Cousin's / cousins' However, you are talking about one, particular cousin in your text, so I'd keep it as "cousin's" for that reason.

iIt was a good opportunity to talk with him. It was a good opportunity to talk with him.

iIt was a good opportunity to talk It was a good opportunity to talk

with him with him

More naturally, I might say "It was nice to be able to talk with him again."

hHe is very relaxing but hed. He lives with his family in Germany ,w. We talked about various topics. He is very relaxed. He lives with his family in Germany. We talked about various topics.

As the three parts of this sentence don't really relate to each other, it's better to break them up.

hHe is very relaxinged, but he lives with his family in Germany ,w. We talked about various topics He is very relaxed, but he lives with his family in Germany. We talked about various topics

To emphasize the distance, if Germany is very far away: "...but he lives with his family all the way over in Germany." Alternatively for the beginning: "He is very relaxing to be around..."

at least wWe drianked a beer and played with his kids . We drank a beer and played with his kids.

There's no need to add an 'at least' here because there's no sense of 'restriction' (at least so far in your writing).

aAt least, we drianked a beer and played with his kids . At last, we drank a beer and played with his kids.

"Drink" has an irregular past tense: "drank". Imperfect past tense is "drunk" (we often use this word to mean that somebody has drunk too much alcohol, too, as in "he is very drunk right now").

We went to the church and we observ, enjoyed the sun and we thinkedthought it was a good idea takingo take a photograph. We went to church, enjoyed the sun and thought it was a good idea to take a photograph.

- In English, you don't need to specify 'the church' unless it is important that it is a specific church that you went to. - Observed the sun is OK, but I think it sounds more like you just hung out and enjoyed the sunshine together. - Past tense of think in this case is thought and the tense was wrong for the subclause.

We went to the church and we observwatched the sun and we thinked it was. We thought it'd be a good idea takingo take a photograph. We went to the church and we watched the sun. We thought it'd be a good idea to take a photograph.

Rephrased much of this to sound more natural. "Observe" has a very serious and formal tone in English. Also, "think" is another verb with the irregular past tense "thought". Imperfect past tense is also "thought".