Is the Arduino ground or the common ground the same as Earth ground? Why or why not?
Q1. Is the Arduino ground or the common ground the same as Earth ground? Why or why not?

Not unless the Arduino ground is connected to Earth ground. In the case of battery powered equipment there is usually no connection between the two. Similarly any isolated mains supplied devices won't have a ground - Earth connection.

Q2. Is the Arduino ground or the common ground the same as Earth ground? Why or why not?

Not unless the Arduino ground is connected to Earth ground. In the case of battery powered equipment there is usually no connection between the two. Similarly any isolated mains supplied devices won't have a ground - Earth connection.