Third-party backup applications can automate this process. Some of these apps allow you to backup not just your progress but also golden eggs and other collectibles, and they work without requiring root access.
Bonus: Facebook sync allows you to compete directly against your friends on the leaderboard.
Yes. is cloud saving, not manual file copying.
On the other hand, you skip the journey. Angry Birds 2 is designed for the long haul. Most high-level players will tell you that the thrill isn't just having a top save file; it's the moment you finally beat a King Pig level that has haunted you for weeks.