I must say that I use anki software to study, and each sentence I have has 2, 3 or more words, so I might have way more than 4000 (I have almot 5905 - around 500 not yet seen, seeing 50 new a day, I also have grammar cards, don't know many, that's why I say my vocab is around 4k).
The news I study I understand fully, because I study the vocab in it. But the news I study are easy and small.
http://headlines.yahoo.co.jp/videonews/
As for dramas, what can I say, I understand and when there's words I don't know I study them. The dramas I watch are easy though and I watch the same episode 2/3 times.