You are using a Thomson TG784 and it should actually do the static IP for you. As soon as you forward 548 to the TC, (which is bridged and using dhcp on internet tab) the Thomson itself will lock the IP address.. but YOU need to make sure this is the case. Make sure you know what the IP is and make sure it never changes.
Getting remote access working is relatively easy from that point. As long as your computer that you are testing from is getting a public IP or you are not behind a firewall blocking access to what is a non-standard port.
The Tesserax method is to port translate.
See method 3 here.
https://discussions.apple.com/docs/DOC-3413
The stuff about the TC itself you can ignore.. but notice how instead of using port 548, they use translation from 8888 to 548. This can help if you have other issues where the ports below 1000 are blocked for instance. But I just use 548.
I´ve tried to access remotely the TC from outside my home network and the time capsule shows up under the shared folder in finder but when I can´t access it.
Also in finder, when I try to go to server and type in my host name (from no-ip.com) I can´t connect...
Ping your no-ip.com address from your computer. ie open terminal and type
ping fredblogs.noip.com (whatever the url you get is).
Firstly does it resolve.. ie does it attempt to ping a real IP.
Don't worry if the ping is rejected.. The Thomson has the ping responder off by default.
(but it may be worthwhile turning on ping responder in the TG784 at least until you know things are working. Just google as you need to do it via command line. )
I want you to make sure the IP that is given to you is the current public IP you get on the Thomson. You can discover that several way.. but the easiest is just to test from the home network.
So test.
http://whatismyipaddress.com/
Find out your home IP address. BTW how stable is it.. does it change every day?? Find out.
So you know your IP address.. 200.100.50.105 (pretend)
Is that the IP you get when you test the no-ip.com address.. if not the address is not updating correctly and will never work because it has not got the right IP.
When you get to wherever it is you do WAN test.. ie from your workplace or internet cafe or whatever.
In finder use Go, Connect to Server.
Type in AFP://200.100.50.105 (not this IP.. your real actual home public IP).
And tell me what happens.