There's no real structure tbh. Basically just come up with at least four (two per person) points of law that support your side of your argument.
From there you can really just follow the good ol' TEEL structure (not even kidding) just have a topic sentence (the issue you want to talk about) then have some explanation of why this supports you, why it is relevant, etc and then while you're doing this insert quotes from the precedent case and the current case drawing similarities.
something to remember is that you can have a point that simply distinguishes between the current case and the precedent case on a point of law (kind of like rebuttal). As for the rebuttal that you would be used to in debating and whatnot, this mainly comes from the questions that the judges will ask you during your submission so basically just be prepared to defend your reasoning when you get asked a question in the middle of a point.
The reason that there's no real rebuttal is because you essentially have no contact with the other team. Unlike in debating where teams make alternating speeches, with mooting, one team presents their case, one speaker after the other, then the other team presents their case. So of course the first team can't really directly rebut any materiel. Again this is why all 'rebuttal' is done thought the judge