There are many different types of PR, because it is a flexible system that may be adapted to the situation of any city, state or nation. The voter selects one party and its slate of candidates to represent them. This type of PR is ideal for large legislatures on state and national levels. Mixed-member smoothly combines geographic, ideological and proportional representation. With preference voting, every vote counts and very few votes are wasted.
Preference voting is ideal for non-partisan elections like city councils.
No, we can't. The one who wins all of the pairwise elections wins. Yes, it could. PR allows small parties to be a credible alternative to voters, giving them a national audience for their views to advance new ideas. An example of this is the German Greens.