1.           HOW TO UPGRADE WINDOWS 8 PRO 64 BIT OS TO WINDOWS 8.1 PRO 64 BIT OS.

2.           HOW TO GIVE ADMIN RIGHTS TO LIMITED USER TO INSTALL WINDOWS SECURITY PATCH UPDATES.

Normally this can be only achieved by downloading it via Windows Store, which requires an internet  connection. But there is a way which will help you to skip Windows Store:

How to download the official Microsoft Windows 8.1 ISO

Regarding your 2nd query:

How to Enable or Disable Built-in Elevated "Administrator" Account Windows 8 and 8.1

Hi,

About your situation, you could upgrade to Windows 8.1 pro 64 bit from Windows store without any problem. This upgrade path is available and you could keep Windows settings, personal files, and applications.

http://windows.microsoft.com/en-in/windows-8/update-from-windows-8-tutorial

For the second question.

If you give the admin permission to limit user, limit user is the same as administrator. In this case, there is no security at all.