I think you understand just fine. In the phrase "I think not" the speaker is just saying "I do not think that is so."
However, I would not start placing "not" at the end of sentances to negate them, that would sound silly. The other phrase you mentioned "She loves me not" is more poetic and not really something people use in everyday speech.
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The Truth:
Johnny Cash could have kicked Bruce Lee's ass if he wanted to.
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