A.

There are 2 ways to do this:

1 - The simplest way, is under "Advanced Features" inside of the "Email Settings" tab there is an option to allow member to use a signature.
When this is turned on, a new icon will appear from the members area called signature, where the members can go to put their signature using the WYSIWYG editor.
The signature will be added at the very bottom of the email.

2 - You can create a Text Area member variable, and then use the member variable ~~ code to put the signature inside of the email.
This method would put the spot for the signature onto the "Profile" page
(instead of it's own page like option 1), but it would be a text area, without a WYSIWYG editor.

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.

If signatures are turned on under "Advanced Features" then yes, the signatures would automatically be added to the broadcasts that you as the admin do on behalf of your contacts.

A. Under advanced features in the email settings you can change the broadcast frequency.  You specify a time period members have to wait between broadcasts.

You also have the ability to specify the limit with a Tool Truck when editing the membership.  When editing the membership you have the option to make it unlimited for that specific membership.

A. Yes, there is a link at the bottom of every email that a person can use to unsubscribe.