They process it same as any other. Nurgle's plagues can infect tyranids, but tyranids devour pretty much everything. They'll likely have some interesting mutations and it won't exactly be easy for 'em, but end result is planet is omnomnom.
There is a TON of biomass there and the losses of bioforms doesn’t matter and they also become immune to the diseases that are on the world so tons of buffs for a little loss
Not that I know of, but I suspect the Great Devourer would only be temporarily slowed down by the offerings from Nurgle's garden, before they got over their tummy troubles and went back for seconds. That's more-or-less what happened with the Imperial virus bomb in Space Marine 2.
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After a long ground war, the first hive ship to taste the planet immediately starts to melt. The rest of the fleet plasma her to death and move on.
Plague worlds are net-negative to the hive.