Everyone will have their own opinions as to when is acceptable to start a horse, but at the end of the day regardless of the age, if the horse is catching on there is no harm in teaching him new things. In my opinion 2 is not necessarily too young to be under saddle, but is
too young for any
amount of heavy work/training. It all has to be light.
I started my mare at 2 1/2 and did basically all walking until she was 3 under saddle. The idea was to get her used to being handled, let her build her muscles slowly and to know the basic cues (again a lot of this was done from the ground too...walking with a bridle on while the trainer was on the ground teaching her to give to the bit) anything under saddle was again light work. From the sounds of it, you're keepi ngit light so far, and that's good.
The way I worked it with my mare was when I first started her out I spent no more than 15 minutes working her on a long line (i handled her 4 times a week but for short incriments whether under saddle or not).
As she got older the time increased as to how long she was being worked for, because a young horse has a small attention span and can only take so much at a time and while their minds mature you also don't want to stress their bodies so keep the time short even though you may be making a lot of progress.
Don't feel bad for asking, I respect the fact that you are at least taking the initiative. I trained my first horse this year and I had help the whole way along from experienced trainers of 30+ years...i still have questions!
Either way, the work you do with him under saddle should be really light, even on a longe line, if he is grasping everything then way as well keep teaching him , but in small time slots.
I am not trying to be rude, and I am sorry if this sounds harsh.
However, if you don't know enough to know the answer to those questions, then you should'nt be attempting to train your horse yourself.
2 years is too young to ride.