I am vastly interested in carthaginian culture (religion, politics and art). However, as is well known, we have few primary sources on those topics. Although I have already acquired a few books on the general history of Carthage (such as "The Carthaginians" by Dexter Hoyos), I would like to know if there is anything that is specific about carthaginian culture. By "culture" I mean mainly philosophy, literature and religion. I'm interested in music too, but I have little hope of finding anything. Could someone recommend specific books, articles or documentaries about this cultural aspect of Carthage? Thanks!
You won't find anything about music. As you said, we have very, very, very little written evidence from the Punic world, much less anything with musical notation.
Hoyos is a fantastic resource. I would also recommend the English translation of Lancel's Carthage (1995) to start. Then Quinn and Vella, ed., The Punic Mediterranean : identities and identification from Phoenician settlement to Roman rule (Cambridge 2014).
For Carthaginian city planning and architecture, look up Kerkouanne (with its many alternate spellings--thanks, French!). As for a specific aspect of Carthaginian culture, it is difficult to overlook the tophet burial grounds and the Carthaginian moloch practice of child sacrifice. Once thought to be a myth, the practice has been confirmed and explored thoroughly via excavation at Carthage by Larry Stager et al.
If you want to get into the Carthaginian mode through the eyes of a French poet, check out Flaubert's Salammbo.