I support @Azbakiyat Amman but keep in mind a lot of the books there are copies. Otherwise, I would say it's worth going on a trip downtown where all the old publishing houses and book kiosks are.
Pomegranate syrup/molasses is sold at any hypermarket or attar. I have never seen Rose Cordial Syrup (Rooh Afza) in Jordan but your best shot would be trying @Asia Market in Jabal Amman across from Abu Jbara