+0
  1. When the bus swiftly slowed down its pace and stopped, Rob immediately rushed on the bus to claim a seat at the rear.

  2. Watching this man, I knew, I never wanted to be on his bad side or be around him when he was having a bad day. just as the doors opened they ran on the bus and started yelling, “When you get off my bus you will form two lines, .....

  3. Mr Brown then got his camera and rushed on the balcony to take photographs.

  4. Creed stepped on the bus, sat down, and stepped on the clutch pedal.

  5. He stepped on the balcony, and he was greeting people he had not seen.

I wonder what "rush/step/run on" in these sentences mean and whether they're all grammatically correct and natural.

I think "rush/step/run on" mean "get on" in these sentences, and they're all grammatically correct and natural.

Am I right?

+1

"onto" is better than "on" in all those sentences.