Question   Is there a certain amount of emails each member's account can broadcast per day or week?

A. Yes, it can send emails to everyone including suspended members. There is an option where you can select if it should include suspended Members or not (and also an option to email only suspended Members).

A. The emails sent by the admin to an Member will show the admin's name and email set under My Personal Info for the reply email.

A. Under Advanced Features in the Emails Settings section there is an option to edit it.

A. Yes, there is a section called "Manage Email Templates" where you can create email templates to use multiple times. 
Once you've added an email template, you can use it by clicking the red email icon in the editor.

A. When logged in as the admin go to "Advanced Features",

Click the "Email Settings" tab, and there is a drop down where you can change the amount.