From my understanding Denuvo runs the exe to tackle any unauthorized tampering. There are a few games where Denuvo as proven to slow down some systems quite heavily and others were the performance drop was very minor. Denuvo claims the impact on performance is zero.

As for your second question, It depends on the Denuvo, either anti-cheat (which is associated with the exe and is thus removed when you uninstall, or you can uninstall it separately) or anti-temper, which can stay.
As per their website:
*Does Denuvo Anti-Tamper leave any files on my computer after I uninstall a game?

Depending on the game, one Denuvo-related file may be left on your computer after you uninstall the game. However, this file is inert and you can either manually delete it or leave it on your system without it affecting your PC in any way.*

Hope it helps.