...improve more and more / better and better...

[Tan Elaine]

By practising hard, we can improve more and more /.better and better our skill in badminton.

1. Is the sentence natural?

2. I believe it should be 'more and more', but is 'better and better' acceptable?

Thanks.

[emsr2d2]

You would "improve more and more" or "get better and better". That's because "to I
improve" means " to get better" so you wouldn't put "better" after it.