There is certainly a difference to my mind as a native speaker. It is subtle and quite difficult to describe, and lies not so much in the direct meaning as the sense. " - with the focus of the question on the person and not so much on the fact that she, in fact, loves someone.
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Hans511) Do you know who(m) she love? VS. 2) Do you know that she loves someone?
2) I feel like there is no meaning difference between them in each number There is a difference in meaning. The first one asks if you know the name of the person she loves.
They have different meanings.
Hans51: 1) Do you know who(m) she loves? VS. Do you know that she loves someone?
2) Tell him who(m) she loves. VS. Tell him that she loves someone.