Should I keep track of my health in some kind of diary or ledger when playing badminton? I want to see if I'm actually getting fitter or not.
Badminton isn't good to asses your fitness. If you want to see how fit you are, do Cooper test max rep pull ups max reps push ups 1 rep max weight clean&jerk 1 rep max weight squat or something alike and see how this evolves over time.
Just be careful not to wreck your back while lifting those 1RMs. By definition 1 rep max is pushing you to the limit of your ability to safely lift a weight. For most people this is very unwise. You can get a good approximation of your strength from 3 or even 5 rep maxes with good form. This is much safer. Unless you compete in weight lifting competitions, there is never a need to lift your 1RM. It is not useful for training and it can hurt you badly. It's all risk and no benefit.
Uh huh. Well, I like starting with recommendations that aren't hazardous. Although to be fair, if people swallow advice uncritically from internet forums then they are going to get themselves hurt sooner or later.
Nice idea. You could test yourself once ever month or so. I would write down my current bodyweight, 100m sprint, box jump, cooper test, ... can't think of anything else right now fitness wise. If you want to get badminton specific you could also record the time of some on court exercise like collecting shuttles from 6 corners or something like that
