"My sister is famous."
Translation:Mia sorella è famosa.
Almost always, yes; the exceptions are mostly singular close family members (mio padre, mia madre, mia sorella, mio figlio, mia zia...) without other adjectives or changes, or idiomatic constructs (casa mia = my home, a mio avviso = in my opinion...). There are also some cases when you can use both, as in "la mia mamma", "il mio papà".
When in doubt, stick to adding the adjective. It is not wrong when it's there, as far as I understand, even when it could be interpreted as being 'cold' or distanced when used when talking about (close) family members. I still prefer that to making the more or less severe error of omission.
I'm not a native speaker, though, so please follow any native advice you may get. ; )
Okay, so your articles are not supposed to be used with your family members. The reason that earlier you could use "il" and "la" with padre/madre is because those sentences were more factual, or trying to explain something. If you are talking about your mother and use an article, you are not putting emphasis on your mother, but rather what she is doing or something of the like. This really only works with "madre" and "padre" though. Otherwise, you don't use an article with family. Then there are some items that you don't use an article with, but we'll get into that later...
There's no article ("la") in the English but sometimes when I translate into Italian and I DO NOT include an article -- even though there isn't one in the English sentence -- my response is marked "incorrect." I'm not sure when to use the article in Italian when it's not used in English. Does it have something to do with possession? Hmmm ...