Well I am staffing right now on one DayZ server
You can't be staff on other communities, if you want to be staff on ZARP.
IF he joins and do that again to player or staff, I give him ban because I told him few times and give him few chances to be better to others and be nice.
You can't ban as a Moderator. If someone is breaking rules, then you can warn them or call an admin to ban them.
You've just joined the server, so i don't think you're ready to be a moderator. Play more throughout the weeks, to get your activity up.