Why radix sort is designed separately as it uses count sort within it and has same complexity also.

Answer 1

I think Countingsort is pretty bad if you have lots of differrent values. If you try to sort a million values that are all different, you will need an array with size a million to run counting sort on it.
Radixsort only needs a handful of different buckets (typically 2 or 10).

Answer 2

ya