Reported speech gives the exact words spoken; indirect speech gives the meaning which was communicated, or of the relevant portion of what was communicated.
Unless your quotation marks indicate that the entire sentences were spoken by someone, none of your examples is reported speech; they all include indirect speech.
He said "I was told that she knows the whole story." ... reported speech
BUT
I was told that she knows the whole story. ... indirect speech
I was told "She knows the whole story". ... reported speech
Bill claimed "She told me that she knew the whole story." ... reported speech
BUT
She told me that she knew the whole story. ... indirect speech
She told me "You fool! You thought you could deceive me, but I know the whole story!" ... reported speech
"I was told," he began, "that you would know this." ... reported speech
BUT
I was told that you would know this. ... indirect speech
Everybody said "Jess is a bright woman, she'll know this." ... reported speech
"She told me you would know this", he grumbled, "but apparently you don't." ... reported speech
BUT
She told me that you would know this. ... indirect speech
She told me "I don't know; but Jess was there, she will." ... reported speech
(I have ignored your alternation of past and non-past; which is appropriate in indirect speech depends on context and is not relevant here.)