I'm not entirely sure how to play this just yet. Can I start playing as a nation after a few turns to make sure I know what I'm doing?
I'd recommend you start at once. It's not that difficult and each turn will take a few days at minimum to a few weeks. Basically it'll go like this: at the start of a turn Lumine will announce what happened in the last turn, say if there is a big crisis that have to be handled in this turn, and give two or three mini-crises to each player (things like natural disasters or budget recommendations;
like this in the last game).
From there you can do whatever you want; you can make statements in the main thread which would be official public declarations or talk in private over PM for things like private alliance negotiation. Then, at the end of the turn you'd post your orders. Usually when I play I have two sets of orders: a public one for things I want everyone to see or that they'd know anyway, like the government's budget or refugee policy, and then a private set I'd send to Lumine with secret things like orders for spies.
Submitting orders at the end of the turn is the only thing you HAVE to do and even with that some players have forgotten a turn and still come out alright. Nothing beyond that is required; roleplaying and public messages are all just fluff to add to the fun.