I think pits have it much worse. Most people have no clue what a Fila is or its temperament.
You asked how hard they are to train, they are pretty easy because they want to please you so badly. However, they can be a bit stubborn. They do need a strong leader but not a harsh one. You have to treat them with kid gloves because they can get their feelings hurt and totally tune you out.
Like most mastiffs they don't need a lot of room. Both of mine are total couch potatoes. My two are the best house dogs that I have ever had, hands down. However, outside and they see something they don't like, they are the hardest dogs I have ever had to control.
I've never heard that they need a special diet. However, I do feed mine raw but not because they are Filas.