You have to have a Domain registered and then forward your domain name that IP. Type "Domain Registration" into google for more info. Alternatively there are a lot of minecraft servers that offer URLs like what you are talking about as part of their service.
That isn't "just stating what you saw" you called the guy a liar. You might not have been trying to be a jack*** but you were one. This isn't about being 1337 or pro or whatever you want to call it, its about manners mate. You don't call someone who is trying to help you a liar simple as that.
Your groups.yml looks fine but your user.yml is a bit funny Try making a new users.yml and just have you in it and see if that works. Then add the users one at a time reloading each time to see which user is breaking it but I'm almost certain that your problem is that you have duplicate user names. Try this:
HOW RUDE! Some tries to help you and you call them a liar! If you actually looked at the site that DeathMarine was so kind to take the time to point you to you would have noticed that it was $0.60 a slot for almost every game other than minecraft which was $3.00 month for the cheapest plan.
If you going to be so lazy, ignorant and rude you aren't going to make it far enough to have a good server anyway I wouldn't bother with it.
That might be how you do it client side but he said that he had his own server. There is a line in the server.properties called spawn-monsters that you can set to false to stop monsters spawning.
Are you using hamachi or are you just running the server on your machine? If you are running on your machine is your friend definitely connecting to the right IP address? You can check your external IP address here