Hi Marie,
Yes some terms can be confusing as the can be used interchangeably.
The term “Rig” usually means an armature object. This is the container that all the bones live inside.
The keyframes you were looking at on the right in your screen shot are the values of the object. The object is staying at 0,0,0, however the “Body” bone is being animated as seen in your Graph Editor.
I can see that you don’t have any keyframes on the object (or it will be yellow). But the reason you have the connected line between the keyframes is most likely that you have keyframed other bones as well. They will be the ones that don’t change value between the keyframes.
But really you don’t need to worry too much about how the keyframes are looking. If it’s doing the right thing, then it’s working.
As for the warning message – Omar is correct.
That is Blender warning you that a script is trying to run when you open the file.
I assure you that it is safe (I wrote it – but it’s just the ui control script). The reason it’s warning you is that technically someone could write something that doesn’t something nefarious to your system.
Let us know if you have any more issues – but hopefully that solves some of the confusion you might be having at the moment.