How to set up a Kickr Core to work with my Garmin, dynamically change "elevations" (resistance), etc
Yes, you can do this with your Edge 820.

You need to pair the Kickr Core to the Edge 820 using the sensor type “Indoor Trainer”.

Menu > Training > Indoor Trainer > Pair ANT+ Bike Trainer

You can “re-ride” a previous activity recorded on your Edge 820 indoors - the Kickr Core will adjust its resistance based on the elevation recorded in the activity.

To do this, choose

Menu > Training > Indoor Trainer > Follow an Activity.

If you don’t have a ride you want to repeat indoors, you can create a course in Garmin Connect and use “Follow a Course” in the Indoor Trainer menu.

This web page at Garmin support gives the steps to connect the trainer to the Edge 820.

This web page at Garmin support gives the steps to follow a course or activity on the Edge 820.

This video from Garmin shows the process of pairing with an Edge 520 and following a course - it's not exactly the same as the Edge 820, but similar.

You can't do this with your Fenix 5X, however.

You can use the Wahoo Fitness app on your phone (connected to the trainer by Bluetooth) if you want to control the trainer manually.