1) The time marker is moved before an actions take place. The rules seem to clearly state this, but in the summary there's a discrepancy with the wording "choose source tray, resolve target tray, move time marker".
This is just reading more into what the summary is actually saying. In Step 1, when you move your action markers you are having to "choose source tray" and "resolve target tray" just by virtue of moving the markers. Nothing more should be read into that.
Step 3 clearly indicates that this is when the actual action is performed.
2) At the end of a round, the active player finishes his actions before the round is concluded. Does the demand tile get flipped prior to or after the actions? This is important because it can influence decisions.
The demand tile gets flipped at the end of the round. But End of Round occurs "after the active player’s turn." So No, the active player gets no foresight of what the demand time will be.
3) At the end of the quarter year, I assume the active player gets one last turn to complete actions before needing to satisfy the people's demands along with everybody else, correct?
I do not follow here... unless it is a continuation of the situation presented in question 2. There is no "one last turn" for anybody at the end of the quarter year. The third demand tile is flipped after the active player completes his turn, then all players must satisfy the demands.