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Should I do a full complete diagram for the main diagram, or just symbolize the inferences I discover on the main diagram?

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Basically I mean apply all the rules so as to create a full diagram using all variables

God no. If you could solve the game outright like that, it wouldn't be on the test. You put in the things that you know have to go somewhere, and diagram the rules. If you end up with two possibilities for a unit and some other key inferences fall into place, it's cool to make two or even three main diagrams if they include substantially different and complete possibilities. The goal should be however to note the variability of the game and diagram it in a way that you can see where things can and can't go. The worst thing you can do is make one diagram with all the variables in it, and convince yourself that its the only way the game can work.