Idiomatic expressions convey concepts and ideas in ways that do not "follow the rules of grammar". That's the way people speak and communicate in every language on the globe. You should learn them. However, you should never feel that you cannot communicate because you don't know all these expressions: if you create your own sentences "following the rules" you will be perfectly understandable. DO NOT LET the "fear of being wrong" prevent you from trying to communicate.
"Io sono" : Literally "I am," meaning "My name is."
This is the normal way to introduce oneself. "Mi chiamo" , which we saw earlier, is less common, used in fairly limited situations when it is specifically required.
"La mia casa": casa means both "house" and "home".
Here it has the meaning of "home".
" Casa mia," "casa tua": my house
Very common expression used instead of "la mia casa". Without the article "la". "Casa mia e' comoda".
A casa mia, a casa tua: "at my house," "at your house."
In my house, your house etc.
A casa: "At home".
You encountered this expression in one of the first lessons.
"In citta'": "in the city"
You will see several cases (not just in Italian) where the use of articles in a variety of expressions does not follow any apparent rule.
piano": "on the third floor"
The third floor in Italy corresponds to the fourth floor in the United States. The first floor is called "pianterreno" or "piano terra" (ground floor), the floor above that is the "primo piano" (first) and so forth.
Il centro is the most desirable, and most expensive location.
stanza .... la cucina..."
one bedroom, the
The use of the definite article is determined by subtle semantic values: here, since an apartment can have more than one bedroom, the number of rooms must be specified. But since one would expect to find only one kitchen and, until recently, one bathroom in an apartment, as well as one cellar and one attic, the usage requires the definite article.