I honestly don't know Tapastic's policy on fan fiction, I'm sure it'd be in the T&Cs. Even if you don't monetise it, it would still be hosted on a site that's making Tapastic money, so there could be a potential issue there that they might want to avoid. But yeah, that's just my guess. At the very least, definitely stay away from any logos or insignias. If you're really worried, you could post a question in the forum about this. Or maybe there's already one with an answer.
As for whether or not the owners of the IP would have a problem. That's very much up to them. Just the other day I saw the Simpsons endorsed something a couple of guys did on Youtube by incorporating it into their own show. On the other hand, Disney and Lucasfilm are notoriously litigious when it comes to their characters. But again, you'd have to be extraordinarily popular for them to even notice or care what you're doing.