In this fanfiction, the TMNT might escape by first observing their captors' routines. If the Shredder has minions guarding them, they could wait for a shift change or a moment of inattention. Donatello might be able to hack into any security systems if there are any. Also, they could use their knowledge of the sewers to find a way out. Maybe there's a hidden passage that the Shredder doesn't know about. And of course, their ninja skills would come in handy for sneaking past guards and making a quick getaway.
Well, in that fanfiction, the TMNT being kidnapped by the Shredder would lead to a lot of action. The turtles would surely fight back. They might start by trying to break free from their bindings. Leonardo would probably try to keep his brothers calm and come up with an escape plan. Raphael would be angry and eager to take on the Shredder right away. Donatello would look for any weaknesses in their prison, and Michelangelo might try to use his humor to lighten the mood and also look for an opportunity to escape.
When writing about Shredder in a TMNT fanfic, you can really play with his character. You can give him new motives or goals that are different from the original. For example, he could be on a quest for a powerful artifact that he believes will make him invincible. His fighting style can be described in great detail, highlighting his skill and ruthlessness. You can also explore his weaknesses, whether they are physical or psychological, which could add more layers to his character and make the story more interesting.
One possible scenario in a TMNT April - kidnapped fanfiction could be that the Foot Clan is behind the kidnapping. They might want to use April as bait to lure the turtles into a trap. The turtles would then have to outwit the Foot Clan's various henchmen and ninjas to reach April. April herself could also show some of her own fighting skills or use her wits to try and escape on her own while waiting for the turtles to arrive.
Well, in this type of fanfiction, the villains who kidnap April can vary. It could be the Foot Clan trying to use her as a bargaining chip against the turtles. Or maybe some new, evil mutant has emerged and sees April as a key to something. The story usually focuses on how the turtles will overcome the obstacles to get her back safely. There are often a lot of action - packed scenes as they battle their way to April.
A possible storyline is that Leo, while being raised by Shredder, forms an unlikely friendship with one of Shredder's minions who has a bit of a conscience. This minion secretly shows Leo the other side of Shredder's actions, the harm he causes to the innocent. Through this friendship, Leo starts to see the flaws in Shredder's teachings. At the same time, he might use the skills he learned from Shredder in unexpected ways to protect those who are in danger from Shredder's schemes.
His personality would likely be more ruthless. Since Shredder is all about power and control, Leo would be taught to show no mercy. He might be more calculating in his actions compared to the Leo raised by Splinter. For example, when facing an enemy, he wouldn't hesitate to use any means necessary to win.
Often, there's a plotline where Leo's kidnapping is part of a bigger scheme against the turtles. For example, the kidnappers might be working for a more powerful enemy who wants to take over the city. Another common plotline is Leo being kidnapped to be used as a bargaining chip, like to get some sort of valuable item from his brothers.