Trouble with the URL direction and Domain forward

I have installed the WP 3.5.1 on my laptop (win7 IIS php 5.2+, mySql).

My laptop connects to my router, which has a public IP address.(e.g. 129.63.16.181, this one is faked). I have set the router and forward port 80 to my laptop.

I registed a domain from godaddy.com. (e.g. example1.com). I forward this name to my router’s IP address. I also registered a domain from cheapnames.com (e.g. example2.com). I forward this name to my router’s IP address too.

Now, if I set WordPress Address (URL) & Site Address (URL) to http://129.63.16.181, then anybody visit my wordpress will have no problem if they type http://129.63.16.181. And everything is fine, I can login in my wordpress too. The only problem is that the webbrowser will display my IP address.

Problem 1: people can either type http://example1.com or http://example2.com to visit my wordpress first page. However, when they tried to login (I gave the user name and password to them), or they want to visit other pages, the example1.com or example2.com will disappear and showing my IP (12963.16.181). But everything is working correct.

Problem2: I tried to set WordPress Address (URL) & Site Address (URL) to either example1.com or example2.com. But when people type http://example1.com or http://example2.com or http://129.63.16.181, they can still visit the first page of my wordpress, however, the default LOGO(picture) doesn’t show up and the css style is not loaded. And they are unalbe to visit any other pages or the pages will not show correctly.

So I have tried to figure it out for two night. But I still have no solutions. Any idea?