"I am a firm believe in what you said that basically once something is on the internet, it belongs to anyone who has the courage to say it's theirs, and it's never off, so it's your own responsibility if you want to keep it to yourself by not uploading it."
It's great that you like doing art for fun and release your work for free use, but the act of stealing somebody else's hard work and claiming it as your own is
100% NOT okay. Most artists upload their stuff to get noticed, gain fans, obtain valuable critiques and feedback, and (in some cases) profit from selling prints etc. It is not usually intended, but some artists also get major job opportunities this way when talent scouts happen upon their work online. Of course, this cannot happen when others steal or reupload somewhere like Tumblr without sourcing. I've even seen people that Photoshop out watermarks, links and signatures and it absolutely infuriates me. People have no idea how much this hurts the original artists. As for not crediting/sourcing, it takes literally 5 seconds to do a
Google image search. Yes, all you have to do is link the image URL and Google will try to find the original source. Somewhere out there, an artist put time and effort into creating something that you enjoy... hours or even days worth. The LEAST you could do is put a minute or two in to try and find the original artist and support them with a link so that other people can enjoy their work too. :\
It's easy to say that you don't care what other people do with your art when you don't depend on it to pay the bills and keep you alive.
As for the original question of this post, yes. Making fan art of existing fan art (or any art really) is okay. A lot of people do this when they're starting out to try and emulate their favorite artists. If you intend to upload however, it is best to give credit where it's due. Obviously a simple signature banner isn't going to do anybody any harm at all, but it would be mighty kind to credit whoever came up with the original idea.