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According to my textbook or dictionary, "to hold sb. cheap" means that you have a low opinion of somebody. In other words, you think nothing of him/her.
See above. I have underlined "textbook or dictionary" because it doesn't make sense. Surely you know whether you found that definition in your textbook or your dictionary. Please be specific. If you found the same definition in both, you need to use "and" instead of "or".
I'm not familiar with the phrase but it seems to me that the first is natural and grammatical, the second is possible, and the third is unlikely.
Perhaps the author(s) of your textbook/dictionary thought they could derive an opposite expression from that. If so, they're wrong. It doesn't exist in English.