My house

I would like a small house that is fully equipped more than a big house with lots of trash in it. 

In the second sentence, you do not need to add "for sleeping," since a bedroom is where we sleep.

I would like to have a bedroom and a bathroom with a shower and a bathtub, like in the picture.

(You didn't have to use a comma "," in your second sentence because you only listed two things. When you list 3 or more, you need a comma "," to list something.)

For example: I would like to have a bedroom, bathroom, and a living room. (living room = 2 separate words)

In the third sentence, you don't need to include the word "around it," because when you say, "a table with six chairs," we already know that they would be around the table. Another very small mistake in the third sentence is the word "mixes." It should be "mix." Remember, present tense verbs all conjugate the same way EXCEPT for he/she/it. You will most likely always add the leter "s" or es" at the end of the verb when you conjugate it to he/she/it. 

Example: I mix, we mix, they mix, you mix, he/she/it mixes.

My livingroom should have a table with six chairs for lunch or dinner, because in Germany, we often mix the living room with the dining room.

The fourth sentence is nearly perfect, just remove the word "but" at the beginning of the sentence and the word "there" in the middle of the sentence. It is weird to start a sentence with the words "but, and, or, etc." in English.

My living room should also have a sofa and a television to relax in the evening with my family.

The fifth sentence is perfect, just remove the comma "," before the phrase "when I am hungry."

I love kitchens, so I want a kitchen with a refrigerator and an oven to cook something when I am hungry.

Sixth sentence, just some minor mistakes. "Sommer" is "summer" in English. You don't need to include "days" after summer because we already know you are referring to summer time.

Sometimes in the summer I like to eat outside, so I would to have a terrace with an outdoor table and chairs.

Last sentence is perfect, just add a comma "," before "there should be."

Next to these objects, there should be a grill for having a BBQ outside.

Very good! Very well written. You only made a few very minor mistakes that I am sure you will learn from. You already speak English very well. I hope I was able to help you out a bit.