If you got no one to practice/train with to what extent do things like shadows, hitting the wall etc. help? they do tend to get repititive and boring and it's not the same as playing on the court. How should one go about such a routine?
Self training can be good provided that you are aware of what you are doing. I can say that doing footwork aka shadow badminton is great for your game provided you are preforming the correct movements to begin with. It can increase your speed and efficiency on court substantially which is very benificial in a game. You can always practice serving which is obviously very important and your serve can never be perfect so thats alway something that you can work on. Hitting against a wall yes it is benificial and well it kinda has its downfalls which is you might develope bad habbits because of not on court hitting but it does help your game in a way like "beat the wall" which is where you play drives against the wall to help your reaction time and working on drives thing that people will say is yes theres no net, your not moving and might develope bad movement but it is still a good thing that you can do. There are other things you can do by yourself im sure but thats just to mention a few, as long as your preforming the correct technique (swing, movements, etc) then you will benifite from it else if you have bad habbits or errors in your movements it will just devlope your flaws more which isnt the best. But i do personally believe that doing things like that can aid your game for sure.
I agree that footwork improves a lot because of shadows but things like anticipating the return are difficult to learn. Many times I am left standing at the base, moving in the wrong direction and unable to read slices.
alot of that comes with experience and experience comes with time. you will never be able to substitute for time and experience.
You can only improve so far with self training. Like others said, without the knowledge of proper techniques, you could unwittingly practice inefficient bad techniques that could also harm your limbs and joints.
In terms of skills, training by yourself is limited. You can practise footwork, play a few wall practices, and practise your serve. But don't forget about fitness training! If you're really motivated and have the time spare, you can improve your game immensely by off-court fitness training.
It's a good opportunity to polish on your footwork and strokes as well as fine tuning your touches and swings. You'll look more natural and effortless.
good point from Gollum as well work on fitness for sure, also do some fast feet drills as well to help your movement on the court so that incase you do get faked out you stand a little better chance of getting there and playing a shot.