Ok, so since that fuse is in the switched position and the radio is still not shutting off, then splicing into the cigarette lighter plug is an easy way to get switched ability. To do it, disconnect the red (ignition) wire coming out of the Alpine from the factory wiring harness circuit and splice it into the dark blue/pink wire going to the cigarette lighter plug instead. (The yellow [battery] wire coming out of the Alpine should remain connected to the factory wiring harness for full-time memory/clock functions). Make sure not to disconnect the black (ground) wire connected to the cigarette lighter.

This should at least get you switched power. The Audio problem is going to be another issue altogether.