I can tell by looking at your blog that you don't understand how custom menus work. Pages are static and are for content that rarely changes. They sit outside of the blog structure and you cannot post to multiple pages in any blog. There is only one main page for posts in a blog and all posts will display on the main blog page. There is no way to exclude posts from the main posts (blog) page.

With WordPress, you use categories to organize posts into subjects and then you can add those dynamic Categories pages created by the software to your navigation using a custom menu.
http://en.support.wordpress.com/menus/
http://en.support.wordpress.com/menus/#adding-category-pages-to-your-menu

Here’s a link to a custom menu walkthrough > http://onecoolsitebloggingtips.com/2011/08/11/wordpress-com-custom-menu-walk-through/

There are many common errors, misunderstanding and misconceptions when creating custom menus and you can read about them here > http://wpbtips.wordpress.com/2011/12/19/custom-menus/

This is guide for creating links in blog posts and pages and it does sound like you are following it.
http://en.support.wordpress.com/links/
This is the general link model:
<a href="URL HERE">Highlighted anchor text here</a>
This is the visual result but as it's just an example it's not actually linked to a page:
Highlighted anchor text here

Enter the anchor text you want to link to first.
Then use your mouse to highlight that anchor text.
Next click the chain icon in the Visual editor and proceed to create the link.

You may want to confirm you are running an upgraded browser version though See http://browsehappy.com and try clearing your browser’s cache http://www.google.com/support/accounts/bin/answer.py?hl=en&answer=32050

If you are still not successful will you please post an active link starting with http:// to a post or page you are experiencing this issue on?
Exactly which "short links" are you referring to?
This is guide for creating links in blog posts and pages and it does sound like you are following it.
http://en.support.wordpress.com/links/
This is the general link model:
<a href="URL HERE">Highlighted anchor text here</a>

I am having problems with adding new shortlinks on my Home Page. Would someone be able to help?

My blog is http://www.talkingbaws.com.

Thanks,

Jonny