First of all it's debatable if viruses are lifeforms, but even if they were, in the examples you listed I think their eradication would be ok (or at lest fair) because it happened by using the means of evolution. Developing an immunity towards these viruses would have happened by random mutation sooner or later anyways. Then it would have taken years to spread among the human race, wich by that point would probably have been dramatically decimated. But the end result, the need for the virus to mutate and evolve in turn to be able to continue spreading is the same. We just spead that process up because we discovered vaccination.
And its not like the virus suffers horribly under bad living conditions in some zoo. It's for all intends inpurposes dead DNA. And if someone wanted to, they could set it free and it would start spreading again among the unvaccinated as if nothing ever happened.
The question about the mosqitos is more tricky. Fucking with the natural eco - balance that has evolved in a certain region over thousands of years can have devastating results and I've never heard of and experiment where introducing a new species or removing one entirely from a habitat didn't fuck things up even more. It balances out over the next few thousand years again, but it still might not be the effect you're looking for. For example how do these mosquitos influence the food chain? Is there an animal dependant on these? That animal would starve. And so on.
A better solution imo would be to genetically modify (e.g. random mutation) these types of mosqitos so that they become unsuitable to carry the illness. Let that spread though the species.
As for the ethics, I don't have a problem with "killing off" viruses, after all I don't mourn peoples cancer cells either, but tinkering with the animal kingdom via planned extinction is not a good idea imo. There's too many factor we don't really understand, and even then effective medicine or vaccines would be much preferrable.







