1. ankle, knee, hip, core, and shoulder stability
2. weight loss
3. we can argue about that
1 and 2 can be combined, I also recommend to combine it with static stretching, that should also fit in well and has an positive impact on the strength of the z disks.
About 3, I’d try to build up some strengths while mostly working on explosiveness. After all, force = acceleration * mass.
For a training like you’re about to go in those conditions, you’ll want your body to be as resilient and stable as possible to prevent injuries. 1, 2, and the static stretching are quite obvious for that, working on the maximum strength also has some positive influence on coordination (within a muscle and between muscles, not hand-eye-coordination), which again should help with resilience. More stable z disks add tension, thus stability. In theory, they should also prevent ruptured muscle(s) (fibers). Explosiveness is just essential for Badminton. Don’t forget to keep stretching and to keep working on your ankle, knee, hip, core, and shoulder stability.
My 1 and 2 would be my first focus to prevent injuries, especially when you already start with regular stretching.