Indeed, no one is really interested in using fake money (aka crypto currencies). But that doesn't mean Taler depends on banking APIs. Taler is a complete digital bank software package and some unofficial regional currencies (most notably a bigger one in Italy) have started using it fully independent of the officially recognized fiat banks or their APIs.

Again, according to the Taler website, the exchange tracks every transaction in order to prevent double spends. If it has a full view of the network, it can employ statistical analysis.

Again, you spend max. 5 minutes browsing the website and now claim you are the expert on Taler 🙄 Just because you track if a token has been spend or not, doesn't mean you can track who spend it, or what on. This is all well explained in the Taler documentation and it has been explicitly designed to be resistant against such statistical analysis.