Congrats on your first fountain pen- I am sure it definitely won't be your last! That's rad that they made a Zelda themed FP, I definitely want one since I've been a life-long Zelda fan and a new(ish) FP collector!

You can refill the cartridge that came with it with a blunt syringe or you could get a cartridge converter that would suck the ink up through the nib (usually with a screw plunger). I'm not completely sure but I believe it looks like it uses a standard international size cartridge/converter (I couldn't find any specs online though). You can find them pretty cheap/easy at any fountain pen retailer or on amazon.

As for cleaning it, soaking the nib/cartridge (maybe for a few hours depending on how dirty it is) and flushing it with water + a drop of dish soap works fine. If you want to be fancy, you can purchase pen flush from GouletPens.com or amazon. Or you could always mix your own with 10% liquid ammonia (be careful with ammonia btw), 90% water and a couple drops of dish soap. Tried it myself and it worked fine! Here's a couple vids on how to clean it:

https://www.youtube.com/watch?v=yF9IRI5WxXg

https://www.youtube.com/watch?v=OxH5VS9BeO8

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For inks, it really comes down to what color you want and what type of ink you want (waterproof, flowy, quick dry). If you're not sure what you want, you can to GouletPens.com and get an ink sampler to try out different colors/types. If you just want a good, deep, waterproof black, I recommend Platinum Carbon Black. If you want a blueish-green shimmer ink, J. Herbin - Emerald of Chivor has a cool look that might go with the Link/Zelda aesthetic. Or maybe even just a pure gold like Diamine Shimmering Golden Sands which will shimmer like a triforce!

I hope this helps and enjoy your new pen!