As the_marq pointed out, "She loves me not" really only works in the context of the famous phrase pair:
"She loves me, she loves me not."
The phrase "I think not." is almost always referring to a previous question, rather than saying "I do not think." For instance, given the question "Is the pizza shop down on the corner open past 12:00PM?" an acceptable answer would be "I think so" or "I think not." These basically shortens the longer answers of "I think it is so," and "I think it is not so."
As you have probably noticed these are older forms of speech and in everyday life you are much more likely to hear "Yep" or "Nope". This particular phrase is usually only used now to give emphasis or flavor to a negative response. Suppose a street beggar propositioned a woman for sex; the response of "I think not," would be taken as more than simply declining the invitation, but as an emphatic and disdainful rejection along the lines of "My sources say no."
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