It's been a very long time since I have setup email servers. That was back in the day when we did not have the luxury of apt and such. Now getting down to your issue.
First thing is we need to know what you are trying to do. Are you setting up a email server so that you can send / recv email or are you just trying to get one of your php scripts to send an email to you.
1) The first thing is I don't think anything should be in your hosts file. Back up your hosts file and return it to the default. Actually your are better off just commenting out everything that was added. I have a running postfix on my box right now and I don't have any of those lines in my hosts file.
2) Check your local ports.
nmap 127.0.0.1 should show smtp.
3) There should not be any reason for all 3 aliases. Also the screenshot you have I am not sure what it is asking for. It says "hostname" not "FQDN". So is it supposed to be just the hostname ??
4) Your dig shows "IN A". That is an address record NOT a MX record. Your commands should be either
dig mx net4u.ddns.net or
dig any net4u.ddns.net
5) Read the "MX Records" section VERY carefully. It states "EXTERNAL" mail exchanger. DDNS does not usually allow people to run internal mail servers. YOU would have to check with noip to find out what they allow and don't allow. I just spent an hour trying to add a mx to my afraid.org DDNS account and could not do it. So you may not be able to do what you want.