I have a late 2015 iMac running OS 10.13.6. Can this be upgraded to 10.14 or any newer OS?

If you want something between 10.13 and Big Sur, see this page:

How to get old versions of macOS – Apple Support

The reason you may not wish to jump all the way to "current" that older expensive apps like Office 2011 and older, or older versions of Adobe Creative Suite, WILL NOT RUN under macOS 10.15 Catalina of Big Sur.

If you need help determining:

1) if you have such older apps, and

2) if there are update options to make the apps compatible,

you can use this free tool:

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

If you have critical apps that cannot be upgraded without significant cost, or cannot be upgraded at all, you should not go higher than macOS 10.14.X "Mojave." It is the last macOS to still support older, 32-bit apps.

It can be upgraded up to Big Sur.

How to upgrade to macOS Big Sur - Apple Support

Yes, you can upgrade your 2015 iMac to the most current versions of MacOS.

The reason I know that is that I am writing this message to you on my late 2015 iMac running Big Sur. :)

Have you had any problems with unexpected shutdowns or the machine auto-restarting after a manual shutdown, because of a kernel panic? Thanks for any reply, yes or no.