I am not able to connect to the App Store on my 2012 MacBook running osX Mountian Lion

that version of macOS is too old to use the Mac app store.

In 2015, researchers discovered that Secure Socket Layer (SSL) Internet encryption was not nearly as secure as was thought, and needed to be replaced. Internet encryption quickly moved to Transport Layer Security (TLS) which was rapidly deployed across the Internet. Over time, sites tightened requirements for what was acceptable for encryption.

Apple issued Safari version 9 in 10.11 El Capitan version of MacOS, which included TLS encryption. It was later provided by Security Update into the two previous versions of MacOS. 10.10 Yosemite and 10.9 Mavericks, PROVIDED you applied all available software updates.

MacOS versions older than those can not make a lot of secure [httpS:] connections on the Internet, because by todays standards, your proffered SSL encryption is considered inadequate.

Best practice would be to install at least 10.11 El Capitan. you can obtain 10.11 by direct download from this article, or if not accessible, readers can provide the direct download link from that article that does not require encryption. A working macOS is required to unpack, Place the installer in the /Applications folder, then start the installation.

How to download and install macOS - Apple Support

use the heading "Use a web browser for older versions"

Hi,

I just wonder if you created or input your Apple ID and password on your MacBook Pro with macOS Mountain Lion.

Once you can make httpS: connections again, everything Internet comes back to life.