All around world, people live.
Correct: There are people all around the world.
Explanation: Not all people live everywhere but there are people everywhere as they travel to different places.

I feel at home on my grandmother's house.
Correct: I feel at home in my grandmother's house.
Explanation: We use in to mean inside a place.

The time is right a to study for ourselves.
Correct: The time is right to study for ourselves

Hello, Sally! Your thinking skill is improving. It's okay if you commit grammar mistakes because they're part of learning. Thumbs up for this! Thank you for submitting your homework! Enjoy your weekend!:)