1: Are buses in your nation required to have seatbelts? If not, how common are seatbelts?
No, but it is recommended.
2: Are people in cars required to wear seatbelts?
Personal choice, but any payment for injuries is decreased if victim was not wearing a seatbelt "for their own damn good."
3: Are motorcyclists required to wear helmets while riding? What about cyclists?
It isn't illegal to go without a helmet, see #2.