When you enter the game for the first time, you will need to register with a Facebook account or an email address to start playing.
Keep in mind that game information, such as statistics and purchases, is associated with the account. This is why you can't change the email address, since all of your achievements would be lost.
On the other hand, if you have created your account with an email address, you can still link it to a Facebook profile later. For this, you must enter the Settings Menu from the upper right corner of your home screen and tap on the "Link" option.
You can also unlink your Facebook account. To do this you need to have an active email address associated with your game account.
We recommend you visit the article: Can I change the email address associated with my account? so you can get more information.