Do viruses compete with each other or even infect each other? (Virus vs Virus)
From what I understand virus on virus action is not particularly common but it isn't unheard of.

Consider the Sputnik virophage which 


  reproduces in amoeba cells that are already infected by a certain helper virus; Sputnik uses the helper virus's machinery for reproduction and inhibits replication of the helper virus.


Also consider the Mavirus virophage, which


  is a double stranded DNA virus that infects the marine phagotrophic flagellate Cafeteria roenbergensis in the presence of a second virus — Cafeteria roenbergensis virus. Mavirus can integrate into the genome of cells of C. roenbergensis, and thereby confer immunity to the population.


As a last example, consider the Organic Lake virophage, which 


  is a double stranded DNA virus that infects the marine phagotrophic flagellate Cafeteria roenbergensis in the presence of a second virus — Cafeteria roenbergensis virus. [...] [It] preys on Organic Lake phycodnaviruses, which in fact may rather belong to Mimiviridae than to Phycodnaviridae.


So yes, viruses do at least occasionally attack viruses and inhibit their infectious potential and grant a sort of immunity. I'm not aware of any applications of this in medicine for now but maybe somebody else can add something to this if they know.