Question   How do I change broadcast feature where I can send out emails whenever i want vs. every 5 days?

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. 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. Yes, you can set a limit of emails that can be sent in a month and the frequency that members can send broadcast messages.

A. No, there is no need for you to stay logged in any longer for all the emails to be sent.  As long as you reached the page saying how many emails are in the que the que will process on it's own without you being logged in.