Have a read of these two links, they should provide you your anwers.
http://social.technet.microsoft.com/wiki/contents/articles/14538.download-and-install-sharepoint-2013-prerequisites-on-windows-server-2012-with-powershell.aspx
http://social.technet.microsoft.com/wiki/contents/articles/14582.install-sharepoint-2013-prerequisites-offline-or-manually-on-windows-server-2012-a-comprehensive-guide.aspx
To your first question first off what is your farm setup looking like??
Where are you ruinning the script from?
Are you saying that it does not appear to start the prerequisitesinstaller.exe on the server? You should see this process in Task Manager if it says Running Prerequisite Installer (offline mode).
http://social.technet.microsoft.com/wiki/contents/articles/14538.download-and-install-sharepoint-2013-prerequisites-on-windows-server-2012-with-powershell.aspx
http://social.technet.microsoft.com/wiki/contents/articles/14582.install-sharepoint-2013-prerequisites-offline-or-manually-on-windows-server-2012-a-comprehensive-guide.aspx
To your first question first off what is your farm setup looking like??
Where are you ruinning the script from?
Are you saying that it does not appear to start the prerequisitesinstaller.exe on the server? You should see this process in Task Manager if it says Running Prerequisite Installer (offline mode).