1) When a citizen is hired or a quest is completed, there are bonus actions granted
Does the player have a choice to NOT use the bonus actions? or is it compulsory to use the bonus actions?
For example, I already have a reserved quest. Then I gained a bonus action of "reserve". I do not want to lose my current reserved quest, can I ignore this free "reserve" bonus action?
All bonus actions are optional, so you could keep your reserve.
2) "All players take an equal number of turns". So if im playing a 4 player game with the first player being player A and game order going from player A>B>C>D, then player D finishes his 5th quest on his turn. Does that mean the game immediately ends with player A,B,C not being able to take another turn?
Yes, that's exactly what would happen.