Chosen Solution

How do I obtain a replacement case for Samsung Galaxy Buds Pro? Also, how can I charge them without the case?

If you want a new official case, you can go here. There is also a replacement 3rd party case here.

Update: You can go through Samsung’s Service Center’s nearest you and purchase a replacement for ANY model! Hope this helps! https://www.samsung.com/au/support/mobil

If I broke my can.i buy a new one

The cheapes option is you can buy a replica/copy of samsung buds plus and throw the buds and charge your buds using the replica case its same as original and dosent damage the buds