Everyone wants to make a strong character. But there are limits to what can and can't (and what should and shouldn't) be done in a fanfiction. The biggest no-no is making your character the strongest in the fanfiction world. If your character surpasses the main character of the story then that's too much. It's not realistic. It really isn't. The biggest turn off for me personally and for other people (that I know of through their reviews of things) is when the OC is immediately the best and brightest. For example, if you're writing a fanfiction in the Sherlock (BBC) or Death Note world then don't give your character better detective skills than Sherlock or L. It's just not believable and while some may argue that fanfictions aren't supposed to be believable, I argue that they should obey the laws of the original work. No one needs an OP (over-powered) OC. And if your OC is that strong then what's the point? Why did you like the original story? For the story, right? The struggle getting there? The challenge? For a perfect character there are no challenges.
Please understand that no one needs to read a redundant past. If your character went through the exact same thing as a character in the original story then your character is vain. I'm sorry to say but that's how it is. If you really want to write a good and strong fanfiction that people will love then make the past original. Try something new. Most of the time people go for a tragic past. Maybe the death of a loved one or a broken heart. That's not bad. It's a start. Now expand and exaggerate as much as possible. Don't just let the character's beloved mother die. Let her die in front of the character's eyes. Let her die brutally. I'm not a sadist, believe me, I'm not, but it's those hurt moments that trigger the feels in the readers. Sorry to refer to the same show twice but if you're writing a Naruto fantiction then please don't make your character a lonely child that was always treated differently because of some great power they had. It's been done. Several times by the original author himself. The past doesn't always have to be sad. It can be happy. Maybe your character has the love and support of their whole family as they embark on their mission. That way they always have someone that cares about them. Someone they can talk to. Overall lesson for pasts: it doesn't need to be elaborate but it should be emotional to the characters and meaningful to the readers.
All the tips from How To Write A Good Story (tab above) apply to this along with some extras. Since this is a fanfiction there are unique appearances. You may be thinking of adding wings to your character or giving them a superpower but if it's not realistic according to your fanfiction world of choice then avoid it. I've read far too many Naruto fanfictions where the author decided to make the character overpowered or overly unique in appearance with the justification that they were Orochimaru's experiment. I'm sorry but the main wings I've seen in Naruto are the hand-like ones growing off of Sasuke's back when he has the curse mark. Not majestic angel wings. Also, if a power doesn't exist in a world don't add it. It'll throw off the power balance along with the logic behind the original story. As for the new Attack on Titan fans I'd advise you stay away from making your OC a titan shifter unless you totally think you have it under your belt. Titan shifters are rare and therefore few. Your character can still be cool (I mean look at Levi, he's no shifter) without being OP.
The lovely thing about crossovers is that you can get multiple favourite characters in one world without having to worry about how they got there. But one thing to keep in mind is that they're all from separate worlds. You may know them all but they don't know each other. So they may be suspicious of one another when they first meet. They may become enemies. They may become friends. It depends on the characters. Also, they only have the knowledge of their world and they only have their abilities. Luffy of One Piece isn't going to be the avatar in The Last Airbender or the Legend of Korra because they already have avatars. Likewise, if Merlin was to enter One Piece he wouldn't be able to stretch like Luffy since he didn't eat the Gum Gum Fruit. So really, it's about keeping the characters in their own minds while thinking of how they'd think about their situation being stuck in a different place with a bunch of other people. Unless the crossover is going to pretend that characters of different worlds have always co-existed. If that's the case then there aren't limits to who can do what since it's all fair in that world. But if that's the case then none of the characters are really themselves any more. Jack Sparrow can be a ninja with ice powers and Elsa can be a pirate with the ability to turn into fire. That messes with their back stories too.