MacBook Pro (10.8.5): apps have no internet, yet the machine does 😳

+1 to @MartinR's guidance.

The fix is to install a newer version of the OS.

The last MBP that could run OS X 10.8.2 Mountain Lion is the early 2013 release. That Mac can be upgraded to 10.15.8 Catalina, and Catalina is (barely) recent enough to be able to run a browser that can still connect securely to internet sites.

You may not be able to connect to Apple servers with Mt. Lion to download a newer OS, but you can use another Mac released thru 2019 or so to download another macOS installer.

How to download and install macOS - Apple Support

Once you have that installer downloaded you can create a bootable USB installer and use that on the old MBP.

Create a bootable installer for macOS - Apple Support

Friendly advice, don't expect to get much more productive use from this old MacBook Pro. It is very vintage and long obsolete. It can still be used for some office tasks (not Microsoft) and other miscellaneous things, but its best internet days are behind it.

Some veteran users here will suggest ditching macOS altogether and installing some flavor of Linux on that hardware. Linux Mint is a popular choice. Linux presents a nice graphical interface and should run just fine on the old Mac, including internet connections and various applications. You should give that some consideration if you want to keep that hardware running.

you are getting great advice. this information is intended to re-state what others have already said, in a slightly different way.

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.

———

Once you have a working MacOS with at least Safari 9, then you can use the 'App Store' links in this article to obtain a later version from the Mac App Store. ONLY the links in this article will provide the App Store versions -- the software has otherwise been "put away" to avoid downloading "by accident".

How to download and install macOS - Apple Support

How to download and install macOS - Apple Support

A lot has changed in the 10 years since the final release of Mt. Lion. I believe the old version of SSL that Mt. Lion used is no longer accepted by most internet sites. It was deprecated in 2015 and replaced by TLS. I would not expect anything earlier than High Sierra to work properly on today's internet, and even its days are numbered.

To obtain, for example, 10.11 El Capitan, you would have to use the version shown in "use a web browser for older versions" section.

once downloaded, you get a .dmg file.

when opened, you see a .pkg file.

when the pkg is opened INSIDE a working version of macOS, that pkg will PLACE the Installer in the /Applications folder (NB>> NOT install it!).