El Capitan Preferences Software Update panel missing

The System Preferences : Software Update panel made its debut in macOS Mojave. In El Capitan, you still need to check the Updates panel in the Mac App Store application. Any prior updates (e.g. third-party applications acquired through the Mac App Store, or operating system updates (point and security releases) would appear in the updates panel.

However, El Capitan is now well past receiving any updates from Apple, and it may be old enough that vendors no longer provide updates because their applications may now require a newer upgrade of macOS than El Capitan.

Nothing to fix, and that 2009 Mac cannot be upgraded further.

I would submit a new post about Mail crashing on that 2009 iMac running El Capitan. Uncertain how to resolve that issue in this reply.

For his Earthlink Webmail browser obsolete issue, it is basically telling him that the security protocols used by that 5-year old Safari 11.1.2 are too old for the sites current security requirements. Earthlink can get the specific browser version from its user agent header that the site receives, and may only be checking the 11 integer value.

The only current browser that works on OS X 10.11.* (El Capitan) is Google Chrome, as it currently supports OS X 10.10 and later. Firefox v83 now requires macOS 10.12. The Earthlink webmail browsing issue should go away with the Chrome browser.