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.
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.
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.
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.
In this fanfiction, Mikey might gain new and unexpected powers. Maybe he could develop the ability to control certain elements like water or fire, which would add a whole new dynamic to his character and the story.
I'm not sure specifically about this 'tmnt mikey gets double mutated fanfiction'. But generally in TMNT fanfictions, double mutation could lead to some really wild and unique abilities for Mikey. It might make him even more powerful or give him some strange new forms.
April and Casey might also be part of this fanfiction. April could use her reporting skills to try and figure out what's going on with Mikey's mutation, and Casey would be ready to fight any new threats that come along because of Mikey's changed state. Also, Splinter, as their sensei, would be guiding them all through this difficult time, providing wisdom and training to help Mikey control his new powers if he has any.