I'm also baffled by this. I couldn't give a rats arse for my dp's ex. I met him 4 years after his divorce, mutual agreement, initiated by her. She is awful, no one but her best friends like her, she frightens her children. She is negative, controlling, spiteful and bitter. Threatened by her, not in a million years.
On the other hand, one of my own ex's dp's felt very threatened/insecure about me. I'm a lover not a hater and it turned out it was because she felt my ex and I got on too well. Oh well.
And as for the facebook thing/birthday thing, OP why are you following her on there......? It's not healthy for you to be that interested, for your own sake, you need to detach from this and block them. Then you will see nothing and it will benefit you emotionally.
This does interest me though, because my dp and I are very tactile, very affectionate, we are always posting up pictures of us together, kissing or looking happy. It amazes me to think that someone would think that that is for anyone else but us. When we are together (as couples who are in love do) we hold hands or walk/sit with our arms around each other, we kiss in public, yes, shock horror in front of the kids.... And twice dp's ex saw us walking holding hands - holding hands I repeat! - and within 5 mins sent ranting texts about us putting on a show for her! Well, we both burst out laughing, if holding hands with your boyfriend is a show, well, she oughta try it. Get a life, better yet, live it. This is her problem, she is clearly obsessing and thinks the world revolves around her, the reality is quite the opposite.