How to use domains?

[admin]

Hallo .
I have a hosting at hostgator.com, and i dont use all the space, and want a new website to incrase my income
So i have thinking about doing something like,
<!-- w --><a class="postlink" href="http://www.mydomain.com/newdomain">www.mydomain.com/newdomain</a><!-- w -->
get it rediret to
<!-- w --><a class="postlink" href="http://www.newdomain.com">www.newdomain.com</a><!-- w -->

But i should still get pagerank to <!-- w --><a class="postlink" href="http://www.newdomain.com">www.newdomain.com</a><!-- w -->

I really dont now anything about this domain thing, but i think this is easy to explain for you guys.

And where is the cheapest please to registere a domain.

Thanks.