Context: The narrator is discussing a keepsake box she got as a present from her father. In this box is where she stores all of the things most precious to her, but I'm not sure if the word "likewise" fits here. I placed it there because the way I see it, her father gave the box to her because she was one of his most cherished possessions, so likewise she keeps her most cherished possessions inside. Make sense? Or is there a better word for this scenario?
I think that the word likewise here is a stretch. I understood why you used it once you explained it but I would never have guessed that's why you used it. If you mentioned it in that paragraph, at the very least, that he had given to her because she was so precious than it could work.
No, it doesn't fit. The phrase "that is why" implies that she cherishes the box. No other word or phrase is needed IMO.
The others are correct. Likewise means in a similar way or manner. For the word to function properly there need to be things in comparison or someone concurring with or repeating another's words or actions.
ditto all of the naysayers above... it would only make sense if you wrote something like, '...likewise, i will give it to my son.'
For me, I wouldn't have interpreted "likewise" to mean this. Therefore, I think a word such as "consequently" or "therefore" might be of more use. Or, you could eliminate the sub-clause entirely, since that is why after the added portion conveys this anyway.