When 真 is used as an adjective, or adverb here in all your examples, "的" can sometimes omitted. When "的" is used however..in my personal opinion it just makes the sentence longer and sometimes you could emphasize the tone on "真的".
When emphasized in an question, it'll feel like you're surprised someone really don't know the subject.
When emphasized in a plain sentence it'll feel like you're emphasizing you really don't know it.
But if you're using it as a noun, then it's just "真"
"不知道這個新聞的真假" (used as noun)
"不知道這個新聞是真的假的" (used as adjective)
"真(的)不知道這新聞的真假" (used as adverb first, then noun at the end)