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The TN is a good option and all occupations are good TN options (depending on your education because there needs to be a nexus between your education and the job): technical writer, (software) engineer, and graphic designer.

You should choose the TN occupational category that will fit your job description and experience/education best.

That's correct and the occupations that I/you listed are all solid TN occupations - meaning generally there's no issue getting them if you also have the appropriate corresponding education.

The TN visa does not have a lottery, unlike the H1-B. It also comes out much faster.