Can I update Safari 11.1.2? At least security? on iOS 10.11.6?

Upgrading MacOS to a later version is an option available if you wish.

1.  Check compatibility

      To confirm compatibility before downloading, check the minimum requirements for

       macOS Catalina, Mojave, High Sierra, Sierra, El Capitan, or Yosemite.

      You can also find compatibility information on the product-ID page for

       MacBook Pro, MacBook Air, MacBook, iMac, Mac mini, or Mac Pro.

      Applications compatibility: https://roaringapps.com