Do you have a perforated circuit board? Do you know how to solder parts and wires together?
The volume control should have an audio taper and not be a linear potentiometer.
Our sensitivity to sound and light levels is logarithmic so that when the volume or brightness control is turned down to halfway, the intensity appears to be half only when a logarithmic audio taper pot is used. A linear pot turned to halfway produces intensity that appears to be turned down only a little.
In my post #24 I said, "The negative terminal of the battery or power supply connects to ground."
A little 9V battery is too small to light 8 LEDs for long. If the music level is high which is turning on the LEDs brightly most of the time then the current from the battery is 160mA. The 9V battery begins at 9V but when it is drained with 160mA its voltage drops to 7.2V in about 30 minutes when the LEDs will be so dim that you can barely see them. I recommend using six AA alkaline cells which last 4 times longer.
The no-name-brand cheap Chinese LEDs have no detailed spec's. Their viewing angle is probably very narrow.