Your question is a bit complicated in wording, so out of all the things we could advice, I need to pick one that matches what I think is your question. Basically I understand you want this:
you type your .tk domain and get directed to the site you have running on a webserver somewhere in your home.
and you currently have this
you type your .tk domain and get your router's login page
Is that rigth?
If that is so, the only thing you need to do is let your router know that traffic comming from outside for your webserver actually be redirected to the right webserver. This means you have to forward a port.
The thing is, your ROUTER has the static IP from your provider. You have a different internal IP for your webserver because you are behind that router. If you forward port 80 (for default http traffic) and possible another port for https (e.g. 443) to that internal IP, you'll be set.
Now it IS possible to do it differently, but I don't recommend this if guessing your experience
- set your server in the so called DMZ
- give your server the public 'external' IP, and route from there to your netwerk (this is weird)
- possibly loads of other options.