Regarding the core of your first question, takeoff is a sensitive "critical phase of flight" where center of gravity can affect the aircraft's ability to rotate.  Generally takeoff has the tightest margin of safety, as you are at your heaviest.  This affects your ability to rotate, as well as your ability to stop safely should there be a malfunction on takeoff.  The movement of people will effect the aircraft's ability to climb out safely.  If you want an extreme example of how center of gravity is important, watch this video: https://www.youtube.com/watch?v=-MB9JDBe4wA - the cargo broke loose and fell aft on takeoff causing the aircraft to pitch up out of control.

For landing, it's generally just important that your center of gravity be within a certain window, which is larger after you've spent all of the fuel over the course of the flight.  

Regarding the bags, that could have happened for several different reasons.  Generally speaking though, the lack of bags would probably move the CG forward, which will probably make the flight safer (again, depending on the circumstances).