More innate socialism/liberalism your game will start with more membership of socialist/liberal and vise versa.
Your minister will also more focus on socialism/liberalism/capitalist/religious too.
This is correct.
Monarchy is a setting that dictates if certain dilemmas and events take place which require that country to have a monarchy, a bit like the earthquakes setting.
Compulsory voting means a 100% turnout on election day, which makes the game play differently and means the party screen is no longer necessary to be honest.