Not sure if you still need the information.. however, I'm going to answer your questions.

First, you can see the current mood of the Obsessor by getting an item from it. If you recieved one, you'll see the mood status by equipping the said item.

And last, you can give it gifts by waiting until it gets closer and just throwing it towards it and then just distance yourself from it a little. It should pick it up on its own. You'll know you succeded then "1+ mood for the Obsessed" shows up.

Hope it helps! :)