Ubuntu 18.04 ASUS ZX53VW keyboard shortcuts, backlight not working

I know this isn't what you want to hear, but you might want to wait awhile. HWE (hardware enablement kernels) should be available for the Ubuntu 18 series around April of 2019. It's been my experience with 16.04 and previous versions that these kernels provide better support for newer hardware (as intended).

Sadly ASUS recommends against installing Linux on this laptop and doesn't appear to be interested in driver development for Linux (at least on this platform).

For more information on the various kernels this page in the MAAS docs gives a nice explanation.

A possible alternative to waiting would be to try a more recent mainline kernel the most recent of which can be found here. Be aware that this could result in unintended consequences so it's prudent to have a backup plan in case something goes awry. Considering that the issues that you are having don't make the system unusable, waiting might be the better option.

Edit Sometimes a BIOS Update can help, but none of the recent updates that I could find appear to address your current concerns and updating a BIOS isn't for the faint of heart and can have the unintended consequence of "bricking" your device.

Note: As I do not have your hardware I cannot provide a better answer than this. Hopefully someone with the ability to test (such as yourself) can provide a better answer in the future.