1. My summer house is in the fiel. I can take a walk. I can play hide-and-seek, too. I can have fun there.

(No problem?)

2. I can raise cows and pigs in a pen.
3. I can pick wild flowers, wild strawberries and mushrooms there.
4. I can have a picnic there.
5. I can play ball with my close friends.
6. I can do snow-fight against my friends in winter.
7. I have a summer house in the field.
8. I have a villa in the field.
(Would you check the expressions above? Is #7 the same as #8?)

"fiel" should be "field"??

Everything is fine except for the use of "in the field." I think you mean "in the country" instead. Make that substitution, and all the sentences will be perfect.

The expressions in sentences 1-8 are all grammatically correct. However, there are slight differences in meaning between sentences 7 and 8.

In sentence 7, "I have a summer house in the field," the speaker is stating that they own a summer house located in a field. This implies that the summer house is likely smaller or simpler in comparison to a villa.

In sentence 8, "I have a villa in the field," the speaker is stating that they own a villa located in a field. A villa typically refers to a large, luxurious country residence. So, this suggests that the speaker's house is more extravagant or spacious compared to a typical summer house.

In summary, while both sentences imply owning a house in a field, sentence 7 suggests a modest summer house, while sentence 8 implies a grander villa.