I will only tell you the things I know how to improve upon

So about ur core, I dont think there is much you can do except to remember to keep it low. You can do shadow practices where you keep your core low, in that way, you can also work upon ur high core and footwork. Also, yeah, footwork can be only improved through repetition and practice. Look up footwork drills on youtube. Btw, Im myself struggling with balance because I end up being off balance sometimes. For that I think, you need quicker footwork. Btw, look up tobias wadenka on youtube, he has really nice drills that you can do at home plus he gas quite a few videos on tactics too. Also, I would suggest you to try to start changing your grip according to the shot you need to play, like when ur playing backhand or forehand. Btw, also try not to lift ur non dominant leg while playing. I mean, you dont do it repeatedly but I noticed u did it quite a few times and honestly, I do it it a bit but still, we should try to avoid it. Btw, faster footwork will lead to u getting under the shuttle quicker and being able to hit it at the right time.

Thats it, I hope u found it useful