Is my iPhone 6 plus, purchased within the last 10 months from Apple through an extended warranty program, compatible with iOS 13 and if not, will it still be functional on the latest iOS 12 and receive security updates?

Your iPhone 6 plus will work just fine after iOS 13 is rolled out. But your phone is too under powered to run iOS 13. You do understand iPhone 6 was released in 2014 and received 5 full years of support. It will be unsupported moving forward. This means it won't get security updates unless there is something critical Apple feels needs to be rolled out to legacy devices.

You're very welcome. If you'd appreciate iOS 13, which should be terrific, iPhone 11 was just announced and will be available this Friday. If you think iPhone 6 is good, you won't believe the upgrades you can get with iPhone 11, starting at $699. It will blow your socks off for sure.

Your device doesn't have the needed hardware to run iOS 13.

It was introduced nearly 5 years ago. Apple sets minimum hardware requirements, and frankly the 6/6 Plus are getting rather old.

The replacement program is completely separate from iOS support.

I misread your original post but I'm sure no iPhone 6 can upgrade to iOS 13.

6S is the minimum.