You cannot open a content  page in VS 2005. You can develop web parts to use on
content pages and you can deploy custom ASPX pages as part of
solutions/features, but these are not Pages in the sense of CMS.

One more question, do I have to install VS on the
SharePoint server computer to develop web part?

That is definitely easier (and it makes it really easy to debug), but it is not
required...

There are tons of articles/blogs on writing custom code in SharePoint, but a
great starting place for web parts is at
www.codeguru.com/.../

Other great resources:
blogs.msdn.com/.../application-development-on-mos\
s-2007-amp-wss-v3.aspx
msdn2.microsoft.com/en-us/library/bb428899.aspx

You can only open the original ghosted pages stored in the 12 hive or
pages that have been downloaded or exported from a site. VS 2005
doesn't understand how to access a page  stored in the database via a URL
address. That's why you get the error you do when try Open Website. If
you download the page from a Pages gallery, edit  it and then re-upload
it you can use VS 2005 to edit the page. But you should be aware that
if you do it this way you won't get a WYSIWYG editor. You will have a
code view.

Although you can edit sharepoint  pages using visual  Studio I really
don't recommend it other than for ghosted pages stored on the 12 hive.
Pages stored in the database should be edited using SharePoint Designer.
It gives a full WYSIWYG editor, a code editor, and full access to Master
pages and CSS style sheets. There is no benefit to be had from editing
pages stored in the database using VS 2005.

Under my SharePoint Designer, the asp.net code is not highlighted, also
the editor does not prompt me or auto finish my typing like in VS. Did I
do something wrong?