It looks like the only issue is the "Access" parameter. Everything else looks good. You'll want to set the "Access" to "Everybody" as it checks the access of the "User" parameter, which subsequently is the user executing the trigger as it's set to to Automatic so it'd be of the newly Registered user. Once set to "Everybody" it should work fine; please let me know if you've any further problems.

Setting From Address to [email] and From Name to [name] should do just that. Please ensure you're using the latest release of CB Auto Actions however. Please note spoofing anther users address won't put that address in the actual emails header, which is likely what your mailing register is using.

Do you have a URL you can supply to your mailer that processes GET or POST requests as a Request action seams most appropriate. Example as follows.

mailregister.com/register.php?email=bob@invalid.com

The above is most ideal for registering users to a mailer as you could do the below with the above example in a Request action.

mailregister.com/register.php?email=[email]