Proxima Centauri is the closest star to the Earth (besides our Sun). If it went supernova, would such an event negatively affect the Earth? Can Proxima Centauri negatively affect the Earth in some other fashion?
First thing, Proxima Centauri cannot go supernova. It is only $0.12 M_\odot$, while core-collapse supernovae can only be triggered by stars that are more massive than $8 M_\odot$. Now the only exception here is if it undergoes a type Ia supernova, but this is very unrealistic because Proxima won't become a white dwarf in trillions of years and is not part of a binary system that is close enough to engage in mass transfer.
To answer your second question, the answer is also no. To affect the Earth significantly, it needs to pass very close (less than 100-1000 AU), which is virtually impossible. Proxima will not approach closer than 3 light years from our Sun in the near future, so it absolutely has no effect on the Solar System. See my answer regarding stellar collisions.