My student's unweighted GPA is 3.4. His ACT and SAT scores are: ACT - 34;SAT - 2080; SAT Math Level 2 - 800. Can you confirm that 34 is in the 99th percentile and 2080 is in the 96th? Should he should report both ACT and SAT?

The College Board publish data in 2011 on percentile rankings for the old SAT which back your interpretation of these scores. The following confirms that an SAT score of 2080 is in the 96th percentile.
http://media.collegeboard.com/digitalServices/pdf/SAT-Percentile-Ranks-Composite-CR-M-W-2011.pdf

An ACT score of 34 is in the 99th percentile.
https://en.wikipedia.org/wiki/ACT_(test)

Unless required your student should only submit the stronger score - the ACT score. The only exception would be where a college requires that applicants submit both scores (like some of the Ivy League colleges).