1. Is the static IP given is public?
Yes, it should be.
2. What is the architecture followed in cable Internet connection?
DOCSIS - Data Over Cable Service Interface Specification
3. How do I map the network I belong to?
That might not be a great idea, they might think it funny to set your DHCP lease time to 300 seconds and force ip address change each time Oh, wait you have a static ip you don't have to worry about that.

Seriously scan their network at your own risk, it's THEIR network.