6. nations with proportional representation tend to have multiparty political systems. nations with first-past-the-post voting tend to have two-party political systems. how do diverse types of voting systems lead to diverse types of party systems?

There are two main types of voting systems that can lead to different party systems.  These are “first past the post” or “winner take all” systems on the one hand and proportional representation systems on the other.  Each of these will tend to lead to a different type of party system.