Question

What sport do you like best?
I like rope jumping best.

What sports do you like best?
I like cricket and dodgeball best.

Which sport do you like better, billiards or squash?
I like billiards better.

Do you play rugby sometimes?
Yes, I do.

Do you play sports on weekends?
Yes, I play badminton with my coworkers every Saturday at the gym.
I have many shuttlecocks and rackets.

Do you work out regularly?
No, I don't. I am too busy.

Don't you want to kill time by taking a walk on the playground?
That's a great idea.

I like handball better than cricket?
What about you?
I prefer cricket to handball unlike you.
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I made sports-related short dialogues.
Would you check them, please?

Answer 1

Shuttlecock is an acceptable word.

The better way to put this sentence is
"Do you want to kill time by taking a walk on the playground?"

You do not need "unlike you".
Just say, I prefer cricket to handball.

Other than those suggestions, your dialogues are fine! Good work!