Why Does It Have White Eyes Why The Large Mushroom?
Acutally Parasect does have some kind of virusy-origins :O
Well actually parasitic. Parasect is described as under the full control of a Parasite named Tochukaso (in real life also known as a caterpillar fungus or to be scientific Ophiocordyceps sinensis). Not going to write an essay on its life, reproduction and everything you can just google that :D. Also apparently its drained of all its nutrients (This gives me the creeps >.<)
The reason why it looks like it is (big mushroom and all) is because the tochukaso has affected its growth making a a more grotesque and wierd version of its pre-evolution Paras.
Its pincers and legs have grown alot larger and the mushrooms on its back grew together into one big, fat mushroom (probably not very tasty either). Its eyes are pure white, apparently resembling those of a zombie and presumably from the influence of the tochukaso.
It doesn't have a virus... that's the way Game Freak designed it, sort of a mushroom insect thing.
Hope I helped! :)