I know mimiviruses and pandoraviruses have orphan DNA - DNA that is not found in other species - but this is DNA that codes for proteins. I am not able to find out if they contain junk DNA. By junk I mean DNA that does not have ANY function at all. Sort of like the junk DNA in the human genome put there by retroviruses, DNA that just sits there, doing nothing, just going along for the ride.
Viruses typically don't have junk DNA-so to speak because of their tiny size. When the particles (of virus) are so small, there really isn't any space for "junk" or extra DNA.
That being said, while viral DNA replication, there may be some errors that may make the virus DNA unable to code for proteins or "junk". While this is an interesting proposition, the mutations that occur in almost cases do not make non functional proteins but mutated proteins which make the viruses more virulent (more true in case of RNA viruses...which mutate a lot faster).
Regarding virus infecting virus, putting its own code it "kind of happens" but not as you would expect. I am listing 2 such examples here-
There are some viruses called satellite viruses and viroids which depend on "donor" larger viruses for some of the proteins they need for replication. This means a satellite virus can survive in a host only if the donor virus is present.
In animals like pigs, when different strains of Influenza virus infect together, while virus assembly genetic material (RNA) of one strain can enter into the other....creating completely novel strain.
Hope that answers your question. Please feel free to ask for clarification. Thank you and have a nice day.