Rich, yes - have samples taken from your body and the number of autophagosomes counted. Not practical for almost all of us.
Not sure if you got a consensus answer to your questions, and there certainly is some debate about this stuff.
1 tablespoon of butter in coffee doesn’t seem to really be going to break a fast, so to speak - i.e. even though there are some calories there, the insulin response will be so low as to be negligible, and your blood sugar isn’t going to be raised, providing you’re like most people.
I think the butter may decrease some of the hormonal benefits of fasting, like more growth hormone, but it’s a matter of degree, and if the butter makes it possible for you to fast, versus not fasting at all, then use the butter and be glad of it.
For autophagy, the picture is at least murkier, with some real potential thunderclouds around. Butter has milk solids in it, including some proteins. Ghee or clarified butter removes most of this problem. Milk solids include one specific protein, leucine, that is a very potent inhibitor of autophagy. 1 tbsp, is still a small amount of butter, and the amount of proteins/leucine in that will be very small indeed. Perhaps a matter of degree here too.