Translation:My apartment is small, however I have everything that I need.
"flat" should be right, shouldn't it?
Yes, it should. Apartment is more used in US English, whereas flat is more used in British English. But people in duolingo somehow tend to prefer the American terms.
If I write: "My float is small but i have everything what i need" it will be correct?
"That" can introduce an explanatory dependent clause. "What" cannot. "That" indicates a specific quality of the object in question, or a subset of a larger set. "What" indicates the object in question itself, or the entire larger set. (you can write: "I have what I need", but not "everything what i need")
And it's not "float", it's "flat" :)
Just to confirm what was said above "flat" is the British English term for apartment
"my flat is small, but I have everything I need" is incorrect O.o I feel like I need English lesson. why can't I use "but" in this sentence? proposed correction says "my flat is small, however I have everything I need"