With System Center Configuration Manager 2012, there is a new functionality: Application Catalog. Using Application Catalog, you can deploy an application on user collection, and all users can use this web page to install or request an application.
To launch the Application Catalog, you can use the existing link on Software Center:
Depends on your system configuration, Internet Explorer can prompt for your login / password. Even if you are in your domain.
However, you don’t understand why Internet Explorer is asking for login/ password. On your SCCM Client policy, you set the right website and add it to the Internet Explorer trusted site:
So, with this configuration, you can think that SCCM Client will configure Internet Explorer with all required parameters.
The issue is due to the Trusted site Zone. By default, this zone does not allow the credential to be send by Internet Explorer. So you have two solutions:
Add your server in the Intranet Zone
Modify Trusted Site Settings by enabling Automatic login with current user name and password
More on Application Catalog
You can get more information about it here.