Hi
Welcome to the forum. Great to hear that you’ve been bitten by the badminton bug. You won’t regret it.

There are quite a few things you can do off court to improve your game.
Good to know you’re skipping,very important for leg strength,stamina and keeping on your toes.
Practicing serves are always a must. Good serves are a vital part of the game.
Paul has some excellent videos on YouTube called armchair exercises,well worth a watch.

The lunge is an integral part of badminton footwork but a lot of players get it wrong.
A simple practice is to hold a shuttle tube at the top in your racket hand. Lunge forward and place the tube upright on the floor.
Make sure when placing the tube that your knee and foot are straight and inline with your arm and that you land heel first.
Keep your none racket foot flat on the floor at more of a right angle to the front for good balance.
Don’t lean your body over your knee and keep your none racket arm out to help reach and balance.
Once you have mastered this you can work out your own routines incorporating steps and chasses and moving to different parts of your practice area.