the snowball doesn't have to do damage it just has to hit the dragon at the right spot on its neck, but you can also use a crossbow, bow and arrow, egg, ender pearl etc.

Is there a discord Server?

It's under the follow button.

Can you close a application and the restart during the speedrun

Can i use show coord

If I’m playing on iOS, can I play with a controller or do I have to use touchscreen?

You can use a controller on a phone, but when you submit a run, you have to put it as a mobile run and not a console run.