I don't know if it's just me, but I don't see you handling many situations.
In your examples, just because a guy said "lalalalalalala" in text chat doesnt mean that they are chat spamming. Chat spamming is basicly sending a ton of messages in a row that make no sense.
Also, like Walrus mentioned, noob isn't a Gigantic insult. Heck, it is even used on some games BY the game company to describe the newer players. That's what it means.
And the big thing is that this needs to be REAL situations that have happened regarding you and other players that required you having admin commands to be dealt with effectively, not just this Ben guy breaking rules constantly and you warning him. You just gave examples on how you would handle the situations. This section made no sense in your application.
Also, verbally asking someone to stop hacking or DDosing is not right. "Hey man, could you Please stop hacking/DDosing? Thanks".
So, there are a lot of things that you need to change on your app, as you barely gave any information on how you getting admin would help your staff duty.
A very forced
Still, best of luck.