The link you have given defines 〜たまま as "remains unchanged". Before examining your examples lets take an ordinary example:
A natural translation would be:
My younger brother fell asleep in front of the television.
A more literal translation, employing the idea of "remains unchanged" would be:
"My younger brother fell asleep while the TV was still on."
Please note that while these two sentences are different in English, they amount to the same thing. But, we had to employ a certain amount of "literary license" to get to what I think you would agree is the more natural English equivalent.
In both your examples your reference has given you the more natural translation. It sounds like you are looking for the "in-between" sentence that gets us from the Japanese to the natural English sentence using the explanation on your link of "remains unchanged". I would suggest:
私の本棚には 買ったまま 読んでいない まんが が たくさん あります
There are many comics (ie manga) on my bookshelf that are unread, just as they were when they were bought. (ie new, in mint condition...remain unchanged from when they were first bought)
In the second sentence:
My younger sister fell fast asleep [unchanged] still wearing her uniform.
We can conveniently use the expression "remains unchanged" here to convey the message that she did not change out of her day clothes (uniform) to her night clothes but this would be to miss the point that translating Japanese requires us to take the unwritten context into account. The situation that remained unchanged was that she did not take off her uniform. This type of expression is often (but not always) used to convey that an action that would normally be done before a second action did not take place.
A more plain use for まま would be:
窓は開けたままだった｜The window had been left open.
話を聞いたまま話す｜tell a story just as one heard it