Is updating safe for my MacBook Pro OS?

See if you can upgrade to 10.14, or 10.15, see sys requirements...

https://support.apple.com/kb/SP777?locale=en_US

https://itunes.apple.com/us/app/macos-mojave/id1398502828?mt=12

macOS Catalina - Technical Specifications

General Requirements

• OS X 10.9 or later
• 4GB of memory
• 12.5GB of available storage (OS X El Capitan 10.11.5 or later)*
• Some features require an Apple ID; terms apply.
• Some features require a compatible internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Catalina:

• MacBook (Early 2015 or newer)
• MacBook Air (Mid 2012 or newer)
• MacBook Pro (Mid 2012 or newer)
• Mac mini (Late 2012 or newer)
• iMac (Late 2012 or newer)
• iMac Pro (2017)
• Mac Pro (Late 2013 or newer)

https://support.apple.com/en-us/HT210190

https://apps.apple.com/gb/app/macos-catalina/id1466841314?ls=1&mt=12

How to upgrade to macOS Catalina – Apple Support

And caution on 10.15, to see which Apps will no longer work in 10.15 get Go64...

https://www.stclairsoft.com/Go64/

On Safari...

Just remember to hit return after pasting this and there is your list of recent email addresses.

https://discussions.apple.com/thread/251212518

Go on the Apple certificate page:

https://www.apple.com/certificateauthority/

Download the Apple Intermediate Certificates

Apple IST CA 2 - G1 Certificate (direct download)

Double click the downloaded certificate to install it in Keychain Access.

You should see it now, in login certificates.

https://discussions.apple.com/thread/251211674?answerId=253087027022&page=1

Try this browser, I much prefer it to Safari in 10.13.6, but Safari works fin in 10.13.6, just hogs RAM like crazy...

https://brave.com/

tioli wrote:

Safari 13.1.2 has been having problems lately and I think I just found out why. Could updating High Sierra 10.13.6 to the latest OS possibly cause even worse problems overall?

Is there a way to be notified when there are updates available? I don't want them to be installed automatically but I would like to know when they're available.

Shall we try to guess what you "just found out"? If it were me I would correct existing problems before upgrading.

Of course it can make it worse.

Sys Prefs>App Store, uncheck auto update.

What is the problem with safari?

OK, take care my friend. :)