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Having extra disk space might slightly affect performance if you are using around 97% or more of the available disk space, but in general those two are not very related.
As for the Droplet plan—am I right in assuming that you resized your Droplet to the new Standard 2GB plan? It sounds like you picked the CPU and RAM only option so your disk space is still that of the old 2GB plan.
The Droplet will still cost you $10/mo if you resize your disk space as well. Keep in mind that a disk resize will take a bit longer than CPU and RAM only, though. See this tutorial for more info on the different resize options: