Today, I'm going to talk about one of my dreams house.

"One of my dreams" sounds like a dream you had while you were asleep, instead of a dream, or hopeful goal, you have for something in your real life. To stress the second meaning, you can be more specific. In this case, "dream house" is a common expression for what you describe.

Also, I want a large and fluffy bed, a wall mounted TV, a decent car, and training machine in the house.

In the future, I want to live in a house that has largea garden large enough for me to have a barbecues with my friends and familiesy.

In "adj. enough to v." the object of the adjective must be the subject of the verb. That doesn't really work with "have" in this sense of "host," because it's people who "have" parties and barbecues.

Also, I want a large and fluffy bed, a wall -mounted TV, a decent car and trainingan exercise machine in the house.

As for cats, I want to get a Russian Blue breed.

"Breed" is already understood, and I wouldn't include it unless I was discussing the breed in general.

I'm going to do my best to make this dream a reality.

In the future, I want to live in a house that has largea garden large enough to have a barbecue with my friends and familiesy.

A person only has one family in most senses, but you can also write "both sides of my family" to refer to the families of your mother and father individually. Also, the grammar "a garden large enough" is always in that order (a [Noun] [Adjective] enough)

Also, I want large and fluffy bed, wall mounted TV, decent car, and a training machine in the house.

What's a training machine? I've never heard of that, it probably has a different name in English. Do you mean exercise machine?

I'll definitelytry to make my room's atmosphere laid-back with dark colored furniture and get two cats and two dogs each.

"Definitely" sounds strange because you cannot ensure the atmosphere will be that way, you can only try to make it that way.

I'm going toll do my best to make this dream a reality.

"I'm going to do my best" is grammatical but not something English speakers would often say, "I'll do my best" is more natural here. "I'll try my best" is also just as good.