Some of these examples are close in meaning. Here are the natural options: He threw his bags onto the floor. (You can use "on", but "onto" is better. Remember that we often use "to" with verbs of transit.) She put her book on the table. (The pattern is "put [something] [somewhere]". "Onto" is possible, but it focuses more on the transition.) She moved towards him. (We need a bit more context, but this is my first choice.)