Where do I unscrew the aerator from my faucet riser pipe?
I would think that the aerator assembly comes off at the lower split that you marked as #1. However with that said it might make sense to try to find a manufacturers diagram / parts list for this particular faucet. Often such document will contain an exploded parts diagram for the complete faucet so you can easily tell what parts attach to others.

It is not clear just what the black covered part of the faucet spout is all about. Is that meant to be a hand hold to be able to swing the faucet spout from side to side? Is it meant to insulate your hand from hot metal parts if you are running full hot water through the faucet. 

The "indentation" at point #2 may not actually be a separable joint at all - particularly if the black part of the pipe covering slides onto the pipe from the end once the joint at #1 is separated.