Answer 1

Pokerus is a disease you can catch by batteling another Pokemon
Basically if you make contact with that Pokemon you will catch pokerus which doubles evs
the chance of finding a Pokemon with pokerus is a 1/3 of a chance catching a shiny according to bulbapedia
If you have pokerus in your team it will spread after a while

Answer 2

It's completely random and is slightly more common then shiny pokemon and seem to appear only once in each game.