If I did something helpful for my district's post office voluntarily(e.g, helping a postman delivering posts for free), can I say "I did volunteer work(or a volunteer activity) in post office?"
Use these:

I did volunteer work at the post office.
I volunteered at the post office.
Students: Are you brave enough to let our tutors analyse your pronunciation?
As a punishment in school, teachers have students come to school on holidays. (They sweep and clean the classrooms and other parts in the school building and outside the building)
In this case, do these examples sound good? And what alternatives are there?
1. You should come to school for volunteering this saturday!
2. I'll put you in volunteering if you keep making noises!
If they have to come, then it is not volunteer work, because it is against their will. In the US, it is called 'detention', though the name suggests that it is somewhat different, since it involves staying after school rather than coming in on another day. Still, I would suggest:

1. You will come to school for detention this Saturday!
2. I'll put you in detention if you keep making noise!