Hello David
Feasible distance and advertised distances are all examined from the point of view of the local router. These comparisons are performed internally and their results are not advertised to other routers. They are used internally only to determine the successor and feasible successor. However, one thing to note is that the advertised distance by definition is actually advertised 
. It’s the value that a neighboring EIGRP router has reported as its distance to the destination in question. Now just to be clear, if you look at an EIGRP update in Wireshark, you will not see the actual metric value, but you will see the various components that comprise it, such as delay, bandwidth, reliability, load, and MTU. It is those values that are included in the update. When that is received by the local router, it will use the EIGRP formula using configured K values to calculate a specific number as the metric. That metric will then be used to compare with the feasible distance to determine if a path becomes a feasible successor or not.
Here is an example of the contents of an EIGRP update message that includes information about a particular prefix:
Note that you can see, under the heading “Legacy Metric” the delay, bandwidth, MTU, reliability and load that comprise the EIGRP metric.
Another way to say the feasibility condition is to say that the “candidate feasible successor router should be closer to the destination than the local router.” Yes, this is indeed used to prevent loops. A potential scenario where a loop could occur might be if a router incorrectly advertises a lower-cost path to a network that actually routes through the receiving router. This could cause the receiving router to start routing packets to that network through the advertising router, creating a loop.
I hope this has been helpful!
Laz