2008 Honda Ruckus fusebox diagram - 2008 Honda Ruckus

Nothing leads me to believe is has a fuse. Also look at the images tab for wiring diagrams.

https://www.google.com/search?q=2013+Honda+ruckus+fuses

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for better result download the pdf file
2003 2007 Honda NPS50 Ruckus Motorcycle Repair Manual PDF

on ebay are sold aftermarket supplies for a air filter, the one you need depends on the opening size you are trying to cover.

could be a relay but check the chain and sprockets for worn links and teeth
if the teeth have sharp points and no fully formed teeth profile it behaves as if the pitch is wrong and the chain will slowly pick up near the tip of the teeth then click back into the sprocket

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Sorry but Nissan diagrams available to up only go back to 2008 models. Try eBay for used owners manual

There shouldn't be any oil on the air filter. Take the air filter out and try drying it out (a blow dryer would come in handy) to make sure the liquid is not water. If it is oil, take it back to the dealer as it is still under warranty.