I bought two domains for my scientific software project,
http://periapsis.pl and
http://periapsis.eu. I have a web server at
http://albireo.vipower.pl/periapsis which is going to be an actual location of the webpage.
So I thought the setup would be rather straightforward, like, an admin panel with some simple form asking me where would I want the domains to point at. But there are too many cryptic options I don't have a clue about

That's how it looks:

There is also another page which lets me create a simple redirection:

Yet, it doesn't work as I'd like to. There are two options there:
- A "visible" redirection, which makes the address change to
http://albireo.vipower.pl/periapsis upon entering the page
- An "invisible" redirection, which makes the address remain as
http://periapsis.pl even after clicking link on the page. Also, all links still have a base URL of
http://albireo.vipower.pl/periapsis, which I'd like to hide from the visitors.
Anyway, my question is, what do I need to do in order to achieve the following objectives:
- when I enter
http://periapsis.pl, the content at
http://albireo.vipower.pl/periapsis shows up, but the address bar doesn't change to
http://albireo.vipower.pl/periapsis- clicking a link on the website, for example
<a href="test.php">test</a>, makes the address change to
http://periapsis.pl/test.php and does not reveal the actual address where the site is hosted.
Can anyone help me with that? Sadly I have no idea how internet works :X