Check plagiarism before submitting to journal
I'll answer question #1: No. Let us not worry about Turnitin specifically, but plagiarism is if you take someone else's text and present it as your own. That is not the case here: You wrote the manuscript, and you remain to be the person who came up with both the ideas and the actual text. It is not plagiarized, and Turnitin will show it as not plagiarized.

There is also no other issue: Since the paper was not accepted by the first journal, you continue to be the owner of the copyright in the paper, and are free to submit it again wherever you want.