Can I cut charger and connect wires to rechargeable speaker wires

Are those wires (Black and Red) connected to the speaker itself? If it does, you snapped the wrong wires. Solder them back to the board. You could solder a connection but the speaker won’t be portable anymore (since the charger is soldered into the board of the speaker). Solder the Positive wire of the charger to the positive terminal (the place where the micro usb connector is attached) and negative to the negative terminal.

Yes just match color code for each jack

Most jack are the same colors just rearanged.as jacks progress so does the number of paired wires.

Sounds to me like ur dealing with a short