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.