I have some doubts concerning a few sentences. I really hope you can check them. Thank you very much in advance.

1)I did rhythmic gymnastics two years ago but I had to give it up to prepare for (?) my school-leaving exam.
2)My favourite book is "Heart of Darkness" by Joseph Conrad.
3) I like wearing baggy clothing (better: clothes). I consider English as (?) the most important language in the world.
4) Last holiday (on/for my last holiday) I went on a cruise in the East of the Mediterranean Sea. I had the possibility to speak English.
5)I like playing "Diabolo" on my computer. It is a game which is based on two poles which attacked a thread that is used to run a sort of double funnel (I can't understand anything here?)
6) I had a turtle called "splash" because she splashed the watr outsidethe aquarium when she was happy.
7)During a football match I'm always agitated (better: excited) because 'm a supporter than never gives up and always hope for a good result for his team.
8) My hobbies are playing with Lego bricks and singing.
9) My father works for
I usually wear jeans and a T-shirt. I play tennis andI sometimes play it with my brother.

7. excited

9. ??

The rest of your sentences are correct. Where you question your choices, any of these are o.k.

1) I did rhythmic gymnastics two years ago but I had to give it up to prepare for my school-leaving exam.

The sentence is grammatically correct. "To prepare for" is the correct phrase to use when explaining the reason for giving up rhythmic gymnastics.

2) My favourite book is "Heart of Darkness" by Joseph Conrad.

The sentence is grammatically correct. It correctly states the title of the book and the author.

3) I like wearing baggy clothing (better: clothes). I consider English as the most important language in the world.

The sentence is grammatically correct, but the word "clothes" should be used instead of "clothing." Also, there is no need to use the word "as" in the second part of the sentence. It should be "I consider English the most important language in the world."

4) Last holiday (on/for my last holiday) I went on a cruise in the East of the Mediterranean Sea. I had the possibility to speak English.

The sentence is grammatically correct. Both "on" and "for" can be used in this context, so either option is correct.

5) I like playing "Diabolo" on my computer. It is a game which is based on two poles which attacked a thread that is used to run a sort of double funnel (I can't understand anything here?)

The sentence seems to have some errors or confusion. It is difficult to understand the intended meaning. It may be better to rephrase it for clarity.

6) I had a turtle called "splash" because she splashed the water outside the aquarium when she was happy.

The sentence is grammatically correct. It explains the reason for naming the turtle "Splash."

7) During a football match, I'm always agitated (better: excited) because I'm a supporter who never gives up and always hopes for a good result for his team.

The sentence is grammatically correct. However, using "excited" instead of "agitated" would better convey the intended meaning. Also, "that" should be replaced with "who" when referring to a person.

8) My hobbies are playing with Lego bricks and singing.

The sentence is grammatically correct. It lists the two hobbies of the person.

9) My father works for [missing information].

The sentence is incomplete. It needs more information to be grammatically correct. The missing information should state where or what company/organization the father works for.

I usually wear jeans and a T-shirt. I play tennis, and I sometimes play it with my brother.

The sentence is grammatically correct. It mentions the person's usual clothing choice and their activity of playing tennis, sometimes with their brother.