Well, sorry for throwing jargon around and confusing you.
An MTA is a "Mail Transfer Agent", which is the same as saying that it is an SMTP (Simple Mail Transfer Protocol) "server".
"Server", in this case, means "program that runs on a computer and provides a service" (in this case, SMTP service) rather than "a computer that provides a service or services".
In other words (MTA==SMTP server) = TRUE.
A program like Outlook would be called an MUA (Mail User Agent), because it is a client program that handles mail for the user . . . it talks to a POP or IMAP server to receive your email, and it talks to an SMTP server to send email to others, but it doesn't actually do the "over the Internet" transfer of mail from one domain to another....
The 0.0.0.0 thing is the "ME" address, used when a service is either running on all interfaces, or on an interface upon which that service doesn't know its IP address. I'd say that's pretty normal, depending on how many ports you have open . . . shouldn't be too many unless you're serving everything plus the kitchen sink.
What do you need to do next? Well, if you're sure that you have mail service up and running, try to get PHP to connect to it by setting SMTP_HOST to its address, etc. Hopefully, it'll return TRUE instead of false when you call mail() now.
As for your next issue, I wish you luck, but I'm gonna have to beg off, as I'm forumming my time away when I have paying clients that need help. Have a nice day, and good luck!