With regard to the giant virus story, there's a lot made of how our immune systems wouldn't be ready for viruses that might come out of the ice. However, it fails to mention that viruses that infected Neanderthal, Cro-Magnon, and other humans in prehistory might not be able to infect modern humans.
Amoebas are simple, morphologically, and don't have much in way of defense against viral attack. Like many microorganisms, their survival strategy tends to be reproducing faster than they can be killed and exploiting resources quickly.
Humans reproduce incredibly slowly, on the order of years rather than of hours. As such, we have a wide variety of defense mechanisms against viral infection. The most basic is a simple inflammatory response; when a potential pathogen is detected, certain immune cells douse the area with indiscriminate toxins, killing off healthy and infected cells alike and cutting off any surviving viruses from new hosts. Specific immunity, where B cells manufacture antibodies that target a certain recognized pathogen, is a secondary response. We might not have defenses specifically against old viruses, but we probably wouldn't need them.
In essence, who needs silver bullets when you have a flamethrower?

Probably not. The "brain eating amoebas", Naegleria fowleri I think are what you're referencing. Unfortunately, "amoebas" are pretty damn polyphyletic, which means that they're actually several different unrelated groups lumped together because they look similar.
The bigger issue, of course, is the issue of delivering the virus. Brain and spinal cord infections are very difficult to treat because of the very reason they're so rare: the blood-brain barrier. That inflammatory response I mentioned? That would wreak havoc in nerve tissue, where healthy cells caught in the cross-fire would be difficult to replace. The membranes surrounding the brain are very very difficult for most things to cross; most medicines won't get across, and even the immune system's cells can't get through usually. A large virus wouldn't stand a chance, so the only way to use it to combat brain infections would be to deliver it directly via injection into the cerebrospinal fluid.